City face sixth-placed Liverpool, fresh from a 3-1 win over Newcastle, at Eastlands tomorrow and manager Mancini doesn't want them to make the same mistake.
"The goal was offside but I've not been to see the referee about it," said Mancini. "I know football, and for this reason, in the last 15 minutes I almost lost my voice shouting at the defence to hold their line and concentrate because of the danger Sunderland posed on the break.
"We seemed to want to attack with 10 players and to do that is impossible.
"I don't know how many chances we had, but I'm not worried about not scoring in the last couple of games, but what I'm worried about is having players on the pitch who understand the situation when we're vulnerable to a counter attack.
"We had chances to score but sometimes when you can't win a game, you make sure you don't lose it."
Sunderland have lost one of five matches under new manager Martin O'Neill, appointed after the northeast side sacked Steve Bruce last month, and their win against City took them six points clear of the relegation zone.
"For us to win the game is extraordinary," said O'Neill. "City were camped outside our penalty area for the last 20 minutes so for us to get players up in support when we broke was unbelievable."
Liverpool, still considering an appeal against the eight-game ban given to Luis Suarez for racially abusing Manchester United's Patrice Evra, could welcome the Uruguay striker back from a separate one-match suspension imposed for a gesture towards Fulham fans following last month's 1-0 defeat at Craven Cottage.
Captain Steven Gerrard is in line for his first league start since October.
For Everton, Anichebe came off the bench to grab his first goal since March 2010, pouncing on a poor defensive header by West Brom midfielder Paul Scharner to score from close range.
It was the Nigeria striker's first appearance since injuring himself on international duty in September.
The win lifted Everton three places to ninth. West Brom remains the league's lowest scorers at home with seven goals in 10 matches.
- AAP