The Spaniard vowed to turn the jeers into cheers having been subjected to the most vitriolic reception imaginable on his first match in charge.
Mancini, in charge of Manchester City, claimed the only way for the former Liverpool manager to win over his new club's supporters was to start winning on the pitch.
"Win, win, win, win, win, win, win, every game – only the results can help," Mancini said.
Benitez said: "It's not a secret. It's true," though he claimed not to have not understood expletive-laden chants which included the words: "You're not welcome here."
"I was asking: 'What were they singing?"' he said. "I don't care. I'm just focused on the game."
When informed what fans had chanted, Benitez admitted he was not surprised following some of the questions at his unveiling on Thursday. "If we start winning games, they will come on board and they will see I'll try to do my best."
He added: "The main thing is that the players are focused on the games. If they are, it'll be fine. I have confidence we will do well and win games. Some of the fans will realise it's not the way to support their team."
Owner Roman Abramovich is the only fan that really matters at Chelsea and Benitez confirmed the pair had spoken afterwards.
"He knows it was a tough game, a difficult time after the last games," said Benitez, who replaced Roberto Di Matteo after a run of two wins in eight.
"He's like me. He knows we have to win, want to win, and we keep working for that."
Abramovich would not have been impressed by a side he desperately wants to be entertained by only mustering one shot on target or by the lack of impact from Fernando Torres, the Chelsea striker.
Benitez said: "You could see he was trying very hard, but the team has to help Fernando and create more chances, and then he will score goals.
"You cannot expect a striker to score just on his own, so we have to create more and better chances for him with the players we have."
Benitez has, at least, stopped the rot at the back after Chelsea went 10 games without a clean sheet before yesterday's stalemate, including Tuesday's fateful 3-0 Champions League defeat at Juventus.
"The team weren't performing at their level in the last games and lost a bit of confidence from the Champions League," Benitez said.
"But this was a clean sheet after so many games. You have some positives. I'm not 100% satisfied because I want to win but there aren't too many teams better than City in the Premier League."
The draw left Chelsea five points behind Manchester United a third of the way through the season.
"Things change all the time," said Benitez, who revealed Gary Cahill missed the game through illness but should be fit for Wednesday's derby with Fulham.
*Dave Sexton, the former manager of Manchester United and Chelsea, has died aged 82.
Sexton led the club to FA Cup glory in 1970 and secured their first European success in the Cup- Winners' Cup the following year.
His managerial career began at Leyton Orient and from there he moved on to Chelsea, before enjoying spells in charge of QPR, Manchester United, the England Under-21 team and Coventry City.
The Football Association's director of football development Sir Trevor Brooking said: "It is a sad day for English football.
"Anyone who was ever coached by Dave would be able to tell you what a good man he was, but not only that, what a particularly great coach he was.
"In the last 30-40 years, Dave's name was up there with any of the top coaches we have produced in England – the likes of Terry Venables, Don Howe and Ron Greenwood. His coaching was revered."