It was City's fourth straight success since Mancini took over from Mark Hughes three weeks ago and followed a 2-0 win over Stoke City and 3-0 win over Wolverhampton Wanderers in the league and a 1-0 win at Middlesbrough in the FA Cup.
NEWS: Tevez treble fires City up to fourth
After praising hat-trick hero Carlos Tevez, scorer Micah Richards and the rest of his team, Mancini told ESPN: "It was a good night for us, but the team must concentrate for 90 minutes and I am angry because we conceded a goal, it was a gift.
"It's important that we concentrate all the time.
"I was angry because it was a gift, but for me we played very well, we must continue to play well and not concede any goals."
The victory lifted City into fourth place and a Champions League spot, taking them to 38 points from 20 matches, trailing Chelsea, Manchester United and Arsenal but Mancini said the league table was unimportant now.
"Now we don't watch the table, we'll watch the table in two months, now it's not important," he said.
Tevez, who joined City from rivals Manchester United at the start of the season and will face them when City meet United in the League Cup semi-final later this month, had a memorable match.
He scored his first Premier League hat-trick and took his tally for the season to 15 goals - with 10 coming in his last seven league matches.
"He was fantastic," said Mancini, who also raved about Richards' stunning goal which came after he ran 70 metres from the edge of his own penalty area before laying the ball off to Benjani Mwaruwari who shot against a post.
However Richards kept running and was first to the rebound, cracking the ball past goalkeeper Paul Robinson.
"It's one of the best I scored, I just kept going and got lucky this time," Richards said.
