Stefano Pioli denied his substitutions were to blame but acknowledged Milan had "messed up" after Roma snatched a 2-2 draw in a dramatic finish to their Serie A clash at San Siro.
Having watched Napoli go eight points clear at the summit by beating Sampdoria earlier on Sunday, Milan looked set to cut the gap once again as goals from Pierre Kalulu and Tommaso Pobega put them in command.
However, Roger Ibanez halved the deficit with Roma's first shot on target in the 87th minute, before Tammy Abraham pounced on a rebound from a stoppage-time free-kick to rescue a point.
The remarkable finale saw Milan fail to win a Serie A match when 2-0 up after 85 minutes for the first time since 2009, leaving Pioli stunned after the Rossoneri dominated the contest.
"We must continue to play like this but remember that matches finish in the 95th minute and that more attention is needed," he told DAZN.
"We conceded two goals from set-pieces which we can't concede. We are disappointed, we played well and we deserved to win. Unfortunately, we messed up our own lives."
In his post-match press conference, Pioli was asked whether his decision to introduce a third central defender in Matteo Gabbia invited a late spell of Roma pressure, but he does not believe the change – or a lack of application from his players – was to blame.
"Oddly enough we conceded two goals from set-pieces when we had more central defenders on the pitch. I reviewed the goal and there were some errors in marking," he said.
"When I make substitutions, I always think they are the best things for the team. We gave away a corner and made mistakes on set-pieces.
"I don't think the tactical aspect has anything to do with it. I don't think we lost points for the three-man defence. Maybe I'll bring it in again.
"It will teach us to stay more focused in the next matches. It wasn't a problem of attitude. If we talk about willpower and spirit, we are second to none."
Roma failed to have a shot on target in the first half of a Serie A game for the third time this season on Sunday, while 48 per cent of their league goals this term have now come from set-pieces (10/21).
Despite the Giallorossi's lack of creativity, Abraham was always confident he would get a chance, telling DAZN: "We had to be patient, this is a difficult stadium.
"We knew that an opportunity could come, I felt it in the finale and I was good. Before the [World Cup] break, I said we would be back in shape, now let's continue like this."