Valentin Mihaila and a Hernani penalty earned Parma their 2-0 win.
Fonseca said, “We should've scored earlier. It was a good start, we had a situation with Edin Dzeko, then the first time they got near our area, they scored a goal.
“A team that wants to be in the Champions League cannot concede those goals. That was a lack of concentration. Parma scored, then they were able to clam up."
Roma seemed exhausted after Thursday's Europa League win over Shakhtar Donetsk.
“I don't want alibis. We cannot concede a goal like that. It changed the game and Parma were then allowed to control the tempo.
“We conceded an avoidable goal and struggled to create chances, which is pretty inevitable when we don't move the ball quickly enough and the opposition is able to sit back.
“We improved once Bryan Cristante came on, but he has played almost every game this season, he needs rest.
“Dzeko worked for the team, he made the right movements, but he wasn't getting the right service. It's not an issue of individuals, but of the collective."