City went down to 10 men in the first half when Fernandinho was given a straight red card for a foul on Johann Gudmundsson.
But Gael Clichy equalised just before the hour mark with a superb right-footed effort, before Sergio Aguero added a second four minutes later.
Ben Mee’s volley with 20 minutes remaining made things nervy for City - but they showed resolve to win the game and move up to third in the table.
“It was a very difficult game, not only for the team we play but the circumstances, which sometimes happens in football,” Sagna said. “I will avoid talking about it (the red card) – I am more focused on the performance we gave in the second half.
“I think we were fighters and it was vital if we wanted to take the three points and we managed to do it.
“We had the fans pushing behind us. Whenever you play against 10, it is difficult.
JOB DONE: The City players celebrate a crucial three points
“We always want more (from the fans). As much as they need us to perform, we need them to support us.
“Believe me, it makes a massive difference when you hear the fans and they put pressure on the other team. It makes their life difficult.”
City are now seven points adrift of leaders Chelsea, who have a game in hand, and just two behind second-placed Liverpool, who drew with Sunderland.
It looks being one of the tightest title races in many years – but Sagna says it’s too early to think about where the trophy will end up.
“It’s way too early to talk about the title,” he said. “We are focusing on the next game.
“Of course, it will be hard to catch Chelsea but we need to stay professional, keep these kinds of performances and we will see.”
City face West Ham United in the FA Cup third round on Friday evening at the London Stadium, a game Sagna believes will be tough.
“It’s never easy to face such a good team but we have to win if we want to go through,” he said. “It’s never easy and we are going to have to give our maximum.”
