Oscar's delightful free-kick earned a 1-0 win over Stoke on Sunday to set up an FA Cup fifth-round tie with City, Chelsea manager Jose Mourinho's favourites for the Premier League title.
Mourinho thinks City, who are in contention for an unprecedented quadruple, have it all to lose after their investments in recent seasons.
But his Chelsea side are in a position to pressurise City, who put their 100 per cent Premier League home record on the line against Chelsea on February 3, after a seventh straight win saw them advance in the FA Cup.
Ivanovic agrees with his manager that City, and not Chelsea, are the ones under pressure.
"Manchester City are playing great football, especially at home," Ivanovic said.
"They must feel pressure. When you know a big game is coming up and you know you're playing at home and must win, it's a different kind of feeling and preparation for the game. We must use that (against them).
"It's going to be a big challenge for us, but we know what we have to do to stop them. It's important we play as a team, to be on top of our game and show more than we do normally to be successful.
"We stay in touch. We know how hard these games will be and how important they will be psychologically. We must be ready for that.
"These are the games for big guys, big players."
Right-back Ivanovic is one of Chelsea's leading performers and Nemanja Matic showed enough on his full debut after re-signing from Benfica to demonstrate he has the potential to be a key cog in Mourinho's team for years to come.
Asked about fellow Serb Matic, Ivanovic said: "He can be a very important player for us.
"He has signed a five-year deal so his future is here, step by step, he will be one of the most important (players).
"He has improved massively from the last time he was here. It's great.
"He is the one who is leading the game, he asks for the ball and looks to go forward. Defensively he has improved a lot too.
"He was my best mate the last time he was here, he is like my brother. We do a lot of things together. It's nice to have him here and it's much easier for me as well."
Ivanovic bade farewell to another friend last week when Juan Mata left for Manchester United.
"It was very sad and emotional for us because he was one of the loveliest guys in the squad," Ivanovic said.
"(But) this was the best thing for all sides. We will see in the future how important it was for us.
"I think Chelsea did a great deal and let a player who is not playing at the moment leave for another club. Manchester United is important for him as a player."
Stoke's attentions now turn to the Premier League, where they face Sunderland on Wednesday.
The Potters are four points clear of the relegation zone entering the midweek fixtures following a five-match winless run in the Premier League which goalkeeper Asmir Begovic hopes will come to an end at the Stadium of Light.
Begovic told Stoke Player: "We're disappointed we're out of the FA Cup. We're going to shake it off pretty quickly.
"I believe in the quality of the team. As long as we stick together and keep believing in what we're trying to do, I think we'll be fine."
Begovic made a number of fine saves against Chelsea on his return from a broken finger.
He added: "The finger's great. It doesn't cause me any problems whatsoever. It was great to be back in action."