Riled Mourinho threatens walk-out
Willian struck a last-minute winner, but the main talking point occurred after Nemanja Matic thought he had scored four minutes from time, only for the deflected strike to be ruled out for offside against Ivanovic, who had blocked the view of Everton goalkeeper Tim Howard.
Tempers flared when Gareth Barry then tripped Willian, earning a second yellow card, and Ivanovic motioned his head towards McCarthy in the resulting fracas.
The Everton substitute was booked for his part in the melee, but Ivanovic avoided censure from referee Jonathan Moss and could face retrospective action from the Football Association.
Mourinho, who was last month fined £25,000 for saying there was a "clear campaign" against Chelsea, was not prepared to discuss the possibility the Serbia defender could be banned.
Mourinho said: "I'm concerned with my reaction, because one more question I leave. And after that you are not happy. The next question for that story I have to go."
Mourinho had earlier told BT Sport: "Did Branislav Ivanovic go in with his head? Don't make me laugh. Don't make me laugh."
And in an interview with the BBC, when asked if he would punish a player if replays showed he had committed an offence, the Portuguese ended the interview, saying: "Sorry. See you tomorrow."
Everton boss Roberto Martinez felt Ivanovic should have been dismissed.
The Spaniard said: "If you look at the images Ivanovic's behaviour is wrong. That shouldn't be allowed.
"He grabs James McCarthy around his neck in a very forceful manner, then he puts his head against him when James McCarthy never reacted one single bit.
"If you want to be on top of the laws that's a red card. We got nothing out of that moment."
The resulting free-kick led to the decisive goal and Ivanovic was involved.
His header was punched out unconvincingly by Howard to Willian, who struck.
Martinez added: "If you want to analyse that action (when it leads to the goal) it's even more hurtful."
Mourinho has already shown his displeasure at Diego Costa being suspended retrospectively for three matches for stamping on Liverpool's Emre Can.
And the Blues boss continues to imply his side are unfairly treated and two decisions went in favour of Everton in the opening quarter of the contest.
Chelsea might have had a fourth-minute penalty when the ball hit Steven Naismith's arm and Everton had another reprieve when Barry fouled Juan Cuadrado and Eden Hazard in quick succession, but was booked only for the first offence.
Mourinho added: "I'm tired of stories and I'm never tired of football. Football is emotion and what we had here today.
"A discussion because of a red card, a red card that should be given in the first half, because Barry should be sent off in the first half.
"He pulled Hazard. The second yellow card should be given there."
Mourinho had no complaints with referee Moss' performance.
"I think it's a clear penalty. I also think the referee had a fantastic performance," the Blues boss added.
"The official that disallowed the goal, it was a fantastic decision."
The Blues were indebted to Petr Cech, who was chosen in goal ahead of Thibaut Courtois and twice saved from Romelu Lukaku, the second when the former Blues striker was four yards out.
Mourinho, who made a point of going to Cech at full-time, said: "He touched the ball twice. He was a spectator. In the first half it's a very good save and in the second half it's a super save."
Mourinho explained Cech was chosen due to Courtois being fatigued and early uncertainty over the health of John Terry, who was ill on the morning of the game.
While the Blues boss had reasons to be unhappy, he was thrilled with the result which kept his side seven points clear of Manchester City ahead of a rare weekend off and a Champions League last-16 first-leg at Paris St Germain.
"I don't remember a team being champions without a couple of victories in the last minute," he said.
"Every time I won a league title we had a couple of matches we won in the last minute. It was the first time this season. So, so happy with the points."
Martinez felt Muhamed Besic's early booking was "soft" and set a standard which was not maintained.
The Toffees boss said: "The first booking after five minutes is soft. And that sets a level. You're thinking there's going to be 12, 13 bookings.
"If you're going to give that level you've got to be consistent and unfortunately that wasn't the case.
"Then Gareth Barry gets a booking. Yes, it's a free-kick, but the player (Hazard) decides to stop, decides to referee the game."
Martinez rued returning to Merseyside beaten.
"The performance didn't deserve to end up with a negative result," he said.
"We produced probably the two best chances in the game. Petr Cech's reflexes were the difference."