The Blues went into the game trailing 1-0 from the first leg but came away 3-1 winners on the night and progressed 3-2 on aggregate.
"When it went to 1-1 we had to score twice but at the weekend we managed to get a 2-0 deficit at Old Trafford so we believed we would get the goals," Cech told ITV.
"Fernando was working hard and he took his chance well. It's a pity the penalty didn't go in for him but we scored the three goals we needed and we're through," Cech added.
"We are at the stage where every game is a final because we're chasing third and have the Europa League and FA Cup. We have a lot of games and it's not easy at times but we'll keep fighting."
Chelsea join fellow Premier League sides Newcastle United and Tottenham Hotspur in the last eight of the competition.