Milan won thanks to a brace from Stephan El Shaarawy.
Tassotti, in charge due to Massimiliano Allegri's suspension, said: "We are happy with the result and earned three points while knowing how to suffer for it. We knew it would be this type of match.
"It wasn't easy to play well with this tension and we've got to try to take the initiative against every opponent, as we are Milan. Clearly we've got to play better than we did this evening, but the team can improve with more confidence.
"The pitch wasn't helping us tonight, as we thought the rain would be enough to wet it, but it was very difficult to play the ball to feet."