Samir Nasri gave City a fifth-minute lead but Spurs hit back with three goals in seven minutes at the death to run out winners, keeping their Champions League hopes well and truly alive.
"We did two big mistakes," Mancini told Sky Sports.
"It's not easy to play here against Tottenham. They are a really good team with good players and a good manager. To come here and played like we did is not easy.
"We played well, we gave a good performance for almost 80 minutes and we had a chance to score the second goal. But we didn't score and after that we did two big mistakes.
"We had the game under control. Tottenham were trying to win because it was important for them, but I think we lost the game through our own fault."