The Aquile took the lead courtesy of a strike from Keita but were pegged back 11 minutes later by a header from Alessandro Lucarelli, with Parma's spirited response leaving the two teams level at the Stadio Tardini.
He told Rai Sport: "It was two point lost, we deserved to win the match.
"However, I congratulate the team. We made a mistake at Parma's goal, which will serve us a lesson.
"The continued rumours about my possible firing? It's just a rumour, no one from the club has said anything to me, I'm calm just like the team."
Lazio are still without an away win in Serie A this season, claiming 13 of their 16 points at the Stadio Olimpico.