Milan had been leading 1-0 at half-time through Zlatan Ibrahimovic, but were held 1-1 by BATE Borisov after a soft penalty.
"I don't know if it was a penalty or not, but the fact remains we should've finished off the game with a second goal," said Ambrosini.
"At international level it can happen that they catch you up. It's certainly a shame, as we had so many chances to make it 2-0.
"Now we'll have to battle for first place with Barcelona, even though it looks as if we'd have to beat them at San Siro to make that happen now. We also wanted to dedicate a victory to Antonio Cassano, but we have been reassured as to his condition."