Vincent Kompany opened the scoring for the visitors in the first half, before Joleon Lescott turned a Charlie Adam shot into his own net to square things up.
With substitute Mario Balotelli sent off late in the game, Mancini is glad to have left Anfield with a point.
“It is a good result, especially because we played the last ten minutes with ten men. It is very important,” the Italian coach told Sky Sports.
“Joe saved the situation but with ten men we had a big, big chance to win it at the end through David Silva. But it was very important to remain unbeaten because it says we are a strong team.
“For us it was a good result because it was difficult,” he stated.
Kenny Dalglish meanwhile felt that his side did enough to claim all three points, but was happy with his team’s display in the stalemate.
“They started better than us but once we got into it, I thought we ran out the better team at the end,” Dalglish also told Sky Sports.
“I think also it was fortunate for us that we got the equaliser as quickly as we did, it kept the spirits up but you could see the change in attitude when we lost the goal that they wanted to go and get something back.
“You could see their attitude in the second half, they were determined they weren’t going to lose it and they tried their very best to try and win it. Unfortunately we just couldn’t get it over the line.
“The performance was fantastic but I don’t think they got what they fully deserved – I think they deserved the three points and we could quite easily have got it but we never.
“But we won’t be feeling sorry for ourselves, we’ll just brush ourselves down and get on with it and see what happens next,” he concluded.
The draw keeps City’s five-point gap at the top of the division, whilst The Reds are in sixth place, three points adrift of the top four.
By Gareth McKnight