José Mourinho has raised the ante on Antonio Conte, appearing to reference the Chelsea manager’s four-month ban for failing to report alleged match-fixing by stating he would never be banned for the practice.

Manchester United’s manager was responding to his Chelsea counterpart’s suggestion that Mourinho is acting as if he has “demenza senile”, which in turn was a response to Mourinho saying he did not have to “behave as a clown on the touchline” to prove his passion for United – which was interpreted as an attack on Conte. In August 2012 Conte, then in charge of Juventus, began a four-month ban for failing to report the alleged match-fixing when head coach of Siena during the 2010-11 season. The Italian was completely exonerated in May 2016.

When asked about Conte’s comments earlier on Friday, Mourinho said: “I don’t blame him. Honestly. I don’t blame him. I think the press should apologise to me and him. Because the question that comes to him is completely wrong and because of that he had that out-of-control reaction.

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“I was asked about my passion and you know I was speaking about myself and then the question to the Chelsea manager was that I said he behaved like a clown. Probably the journalist wanted to say that but didn’t have the courage so he said Mourinho said you behaved like a clown.

“I understand his reaction. I was speaking about myself saying I don’t need to behave like a clown to show passion. I control my emotions in a better way. Everybody knows, I don’t need the Chelsea manager to say I made mistakes in the past. And I will make in the future hopefully. I celebrated goals running 50 metres, I celebrated goals sliding on my knees, celebrations jumping in the crowd. I’m not free of that, especially if we score a winning goal in a specific moment I am not free to have an out of control reaction.

“What I was trying to say is that I behave bad a few times and this moment I control myself better. It doesn’t mean my passion is not the same. So wrong question and obviously a strong answer and I don’t blame. The only way I want to end the story is: yes, I made mistakes in the past on the touchline and yes, I will make less but I’ll still make a few. What has never happened to me and will never happen is to be suspended for match-fixing. That never happened to me and it will never happen.”

During the case Conte continually denied the allegation and in May 2016 Judge Pierpaolo Beluzzi said Conte had been acquitted because the accusations of sporting fraud were baseless.

Asked to clarify if it was Conte who he referred to, Mourinho said: “Sorry?”

Put to him again that he mentioned match-fixing and that Conte was charged with failing to report it, the Portuguese said: “Did he? Not me.”

Earlier on Friday Conte had launched a fierce attack on his rival. The Chelsea manager has never been so outspoken at a press conference in England and he warned Mourinho to watch his words in future. Otherwise, as Conte made plain, he was ready to fight with him.

There is no love lost between the pair and Conte felt his patience snap after hearing Mourinho’s “clown” comments on Thursday.

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Conte bit back strongly, reminding Mourinho that he could be similarly animated during his younger days. Mourinho famously ran along the Old Trafford touchline in 2004 to celebrate his Porto team’s Champions League winner against United.

“I think that he has to see himself in the past – maybe he was speaking about himself in the past, yeah?” Conte said. “Maybe sometimes I think that someone forgets what they said in the past or which is his behaviours and sometimes I think there is, I don’t know the name, demenza senile, when you are a bit [Conte taps his temple] – when you forget what you do in the past.”

Conte switched to his native Italian to find the phrase he wanted – it translates into English as senile dementia, although Chelsea later insisted he meant to say amnesia. Conte continued: “It’s when you forgot what you say in the past, your behaviours, when you totally forgot. You must be worried when this happens because it means you are becoming old and you need a [medical] check.”

Conte clashed with Mourinho last season, after Chelsea’s 4-0 win over United at Stamford Bridge. Mourinho had taken issue with Conte’s attempts to gee up the crowd when the result was long settled and there have since been a few instances of back-and-forth between them.

“You must have respect and I think I do but, at the same time, I am starting to be a bit annoyed,” Conte said. “The people who know me very well in Italy [would say], for this reason, you must pay great attention when you speak because, if you want to go to fight with me, I am ready. I have zero problems. I am improving a bit my English because this is the real problem for me. Otherwise we can go to fight. I’m ready to fight for me, my players, the club – with everyone. I have no problem.”

Conte brought up how some managers were synonymous with turning their press conferences into grand shows and how this was not his style; it was easy to consider this as a dig at Mourinho.

“I am not prepared, like other persons, to make a cinema because there are other persons who prepare to have a cinema in the press conference, before the game and during the game,” Conte said. “I am not this type of person. At the same time, when I start to listen with regularity to this situation, it is right to answer because it is funny and I laugh a lot.”

It was put to Conte that dramatic press conference performances might be a means of diverting attention from disappointing results. “I don’t know – now it is very difficult to do only cinema,” Conte replied. “Maybe in the past with the cinema, it was enough. Now you have to show football knowledge and the cinema is not enough for the coach.”

Conte also turned his fire on Arsène Wenger, who had said on Friday that Eden Hazard ought to have been booked for diving in the 2-2 Premier League draw at Arsenal on Wednesday night. Instead, Hazard was awarded a penalty, from which he scored.

“I think if Arsène Wenger watched the game again, [he should] understand that he was very lucky during the game for refereeing decisions,” Conte said. In addition, Conte would reference Arsenal’s fortune with refereeing decisions in last season’s FA Cup final. Arsenal beat 10-man Chelsea 2-1 and Alexis Sánchez’s opening goal came after he had got away with a handball.

Conte was asked whether it irritated him when rival managers talked about him or his players. “It is very strange,” he replied. “Because I don’t like to speak about the other coach, the other players. I think that is a form of respect you must have and, I repeat, sometimes, for example, Wenger forgets that in our last few games [against Arsenal], we finish with 10 men. When they won the FA Cup and Community Shield, the referee decisions were a bit strange, you understand?

“I can talk, if I want, about referee decisions for one month but I don’t want to do this because we must have respect for the decision. Also, Wenger tries to find this way like other coaches and it is not good. You have to accept the decision. He is an old coach, he has experience, he won a lot and he has to continue to do what he did in the past.

“For the other situation [with Mourinho], I am repeating – there is a person who continues to look here. He went away but continues to look here.”