The 42-year-old is disappointed that the match will be remembered for its officiating rather than the football it served up, but nevertheless happy his team rescued a point
The Old Lady bagged a late point courtesy of substitute Alessandro Matri, who cancelled out Antonio Nocerino's early strike, but the game was overshadowed by a pair of questionable refereeing decisions in the form of two disallowed goals from Matri and Sulley Muntari.
A half-time bust-up between both clubs also ensued, and Conte could only apologise for the controversy that unfolded at San Siro.
"These things happen, and I'm sorry that this match had too much tension," he told Sky Sport Italia after the match.
"There was not a beautiful atmosphere for the purists. Too many things happened that were not football-related, and I did not like them.
"The best thing was the game itself, the rest should be improved in the future. I, for one, must also improve."
Conte then backed Alessandro Matri's view that both incidents cancelled each other out, but attacked former Milan midfielder and Sky pundit Zvonimir Boban, who claimed Muntari's header held more significance to the final outcome of the match than Matri's offside finish.
"There were two serious technical errors on two goals from Matri and Muntari. These are errors that can occur, but they are both even," he continued.
"We hope that errors can always be balanced for and against all teams come the end of the season, but I find unacceptable to say that a goal is more regular than the other."
However, despite the negativity surrounding the game, Conte praised Milan for successfully putting his team on the back foot for the first hour, but was pleased the Bianconeri responded thereafter.
"We must credit Milan because they played at a very high level for an hour, putting us under intense pressure," he stated.
"But it was unlikely that they could sustain it for the entire match and we were good at exploiting them, aided by the players I brought on.
"The people watched a great Milan team, although they missed many important players. We were both good and lucky, but there is still much to do for the Scudetto."