Manuel Pellegrini said Manchester City’s 3-0 victory over Chelsea on Sunday was the “least we deserved” despite José Mourinho’s claim that the 3-0 scoreline was “fake”.

City thoroughly convinced against the champions at the Etihad Stadium. The Chelsea manager was moved to replace his captain, John Terry, at half-time, the first occasion in 177 matches Mourinho had done so. Sergio Agüero’s 31st-minute goal was followed by others from Vincent Kompany and Fernandinho on 79 and 85 minutes to complete a result that opens up a five-point gap for City over Chelsea after two matches.

When it was put to Pellegrini that Mourinho had described the result as “fake”, the City manager replied: “In the first half we deserved at least three goals. It was more equal in the second half. Chelsea played better but I just remember Joe [Hart] making one save at 3-0. Our team played better and three is the least we deserved.”

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Mourinho said: “The best team in the first half won the game. The best team in the second half was Chelsea, for sure. We had a difficult first half. We didn’t create a lot and our goalkeeper made a few important saves. If the 1-0 was a doubtful result at minute 70, 3-0 is completely fake. At 1-0 Chelsea were the best team for the whole second half. They make a change because they feel 1-0 is in danger and we concede a second goal. If 1-1 [it’s] a different story, their team is in trouble.

“I don’t analyse the opposite manager’s work but no one will misunderstand me if I said we played well but he [Pellegrini] felt the result in danger. He made a controlled change for Nasri on for Navas and a defensive change, Demichelis for Sterling, so at this moment everyone knows the 1-0 is a result they want to keep.”

Pellegrini was pleased with his side’s performance but believes City’s points advantage over Chelsea is immaterial. “Nothing is significant until the end of the season. We were in the same position in January but lost by eight points at the end. The gap is important but we are just starting and not sending a message.”

The Chilean, who has not ruled out signing Valencia’s central defender Nicolás Otamendi, went on to hail the influential Agüero, saying that last season’s golden boot winner can improve. “Sergio is in the best moment of his career. This year I think he can be even better,” said Pellegrini.

Kompany added: “As a defender scoring is not what I take most pride, but I am really happy with the two clean sheets – that is what makes me sleep well at night.”

Mourinho’s side have only a point yet he insists the current squad can retain the Premier League and win the Champions League. “Yes,” he said, though he did admit concern over Chelsea’s rearguard. “We were fragile defensively. When the game starts and 10 seconds later you have Agüero behind the defensive line and facing Begovic, immediately you have the notion the start is not good and he made three saves because of that fragility. But that is football.”

Mourinho, whose signing of the left-back Abdul Baba Rahman from Augsburg was confirmed by Chelsea, tried to brush off substituting Terry for the quicker Kurt Zouma. “I don’t know if you ask Benítez, Roberto Di Matteo who never play him,” the Portuguese said of the former Chelsea coaches. “I am the one who plays him every game, and recovered him in difficult moments with others managers, and the one who has the right to look at the game and say I want Zouma on the pitch.

“When I am losing 1-0 and trying to anticipate what I am going to do it is clear to me Zouma is going to play and I have to bring one out. I take off my captain but he is still my captain but the armband is just an armband.”

Asked how Terry had responded, Mourinho said: “I can tell you he was not dancing in the dressing room and he was not having a bad reaction. He did what everyone does. This player comes in and this player goes out. They wait for the team to go out and then go back to the bench like he did.”