Villa then went on to wrap up a comfortable victory, leaving City without a goal from their last 6 home games.
"The missed penalty was certainly very influential," said Pearce. "We started very brightly until they scored, but the penalty affected our confidence badly because there's a bit of pressure building up with us not scoring at home for a while, and that's all adding to the mix.
"We have to make sure we are a touch stronger than that. If we had gone into half-time level, I think we would have won the game but we look nervous at home at the moment.
"Obviously we're disappointed with what we have done at home since Christmas," added the City boss. "It's held us back drastically and we know we need to improve that.
"We've managed to do quite well on the road, playing a counter-attack style of play, but sustaining pressure on the opposition when they are sat back has been difficult for us."
City's final home game of the season is against United on Saturday (12.45pm ko), with the Reds on the verge of clinching the Premiership title.