The Belgium international has had a good start to his Anfield career, having joined in the summer, but his failure to deal with Alvaro Negredo's shot ultimately led to City winning 2-1 at the Etihad Stadium on Boxing Day.
Liverpool had led through Philippe Coutinho's 24th-minute strike but, after Vincent Kompany's headed equaliser, Mignolet got a full hand to Negredo's shot on the stroke of half-time but still allowed it to bounce past him.
"It is one of those things that happens, unfortunately, when you are a goalkeeper. Any goal you concede is a disappointment," he told Press Association Sport.
"I probably should have done better with it. I've been there in the past as a goalkeeper and you have to accept it and move forward to the next game.
"It was a very awkward moment for us just before we went into half-time.
"It gave them a lift and we went in being down but then again in the second half we lifted our heads and tried to create as many chances as we could."
Mignolet said despite his mistake there was no blame culture in the dressing room and the squad remained united in their support for one another.
"You always win with 11 and lose with 11 and more importantly also with the people on the bench," he added.
"We don't want to look for excuses because every game you lose it is always up to you and it is your team performance which counts but we can gain a lot of confidence from this game.
"I thought we played well and created a lot of opportunities but unfortunately we came out with a defeat rather than the three points because I think we had chances to win the game.
"We can certainly take positives out of this game moving forward to the Chelsea game at the weekend.
"We have to make sure we prepare ourselves for Chelsea and do things right there."
Defender Glen Johnson offered his support for Mignolet.
"He has been fantastic all year," he said. "He is a strong lad and mentally tough. Everyone makes mistakes."
The England right-back felt the performance against City, who have now won all nine of their home matches this season, showed they could compete with the teams who are established Barclays Premier League title and top-four contenders.
Had decisions gone their way the result could have been different with Raheem Sterling having a first-half goal disallowed despite being well onside when he made his run.
"You can't defend the lino - it's ridiculous," he said of the offside decision.
"You've heard commentators defend officials in the past when the players are on the same bit of grass but they are three yards apart, it's not even close."
Johnson added: "We dealt with most things well and we had some good chances and that is why we are disappointed we haven't got more than we have."
Next up is Johnson's former club Chelsea, who also have an impressive home league record.
Back-to-back defeats would be a significant blow to a Liverpool side which is now fourth, having been top of the league on Christmas Day.
"No team fighting for the top four wants to lose two games in a row," Johnson added.
"We will get over this and we will be as positive as you can be with a defeat and move on to Sunday.
"On our day we can give anyone a game. We know we have the quality to be up there.
"We played well it is just a shame we didn't get at least a draw."