Pep Guardiola believes that Manchester City’s 3-0 Carabao Cup final win over Arsenal at Wembley can fire the club’s push for a treble of trophies this season.

The manager said the victory, secured with goals from Sergio Agüero, Vincent Kompany and David Silva, represented payback for the club’s owners for the support they gave to him last season. Guardiola will now push to add the Premier League title and the Champions League trophy.

His team are 13 points clear at the top of the table, with a game in hand over second-placed Manchester United while they are 4-0 up from the first leg of their Champions League last-16 tie against Basle.

The manager also adopted a defiant tone against the Football Association, in the wake of his charge for wearing a yellow ribbon in support of imprisoned Catalan politicians.

Guardiola wore the ribbon at Wembley and he said that, even if he was banned from the touchline by the FA, he would continue to do so. But this was primarily an afternoon in which he could celebrate the first silverware of his City tenure.

“Winning titles helps you to win more, that’s true,” Guardiola said. “My players know we will not go far in the Champions League if we play like we did in the first half here. But we showed who we are in the second half. We played really well from the first action.

“Big congratulations to everyone at City – from Sheikh Mansour, Khaldoon [al-Mubarak] to everybody else. I can’t forget how they took care of me last season when it wasn’t so good. I will always remember how everyone at the club, like Khaldoon, supported me.”

On the yellow ribbon Guardiola added: “They [the FA] know I will wear it always. I can wear it somewhere else. Uefa have another opinion. They say you can wear it as long as it’s with respect. Here [in England] it’s different apparently.

“I have empathy for the people who have no freedom, those guys in Spain who are in jail. They haven’t been proven guilty. Anyone can be in that situation. Before being a football manager I am a human being and this is for humanity.

“There are four guys in prison and other guys, they don’t have weapons, just votes in the ballot. I said this is always with me and it always will be until the last. I will accept whatever they [the FA] decide about my behaviour. It’s not a lack of respect, it’s being part of humanity.”

The Arsenal manager, Arsène Wenger, lamented an early missed chance – even though Pierre-Emerick Aubameyang appeared to be offside – dismal defending on the opening goal from Shkodran Mustafi and the lack of an offside call on City’s second, when Leroy Sané appeared to be in David Ospina’s line of vision.

“A little bit of everything went against us,” Wenger said. “We self-inflicted our punishment. The second goal is offside. It’s a mystery how it cannot be given.”