Giovani Lo Celso scored the second goal in sublime fashion having set up Antonio Sanabria's opener as the La Liga visitors eased into a two-goal lead at San Siro.
The Rossoneri struggled to find a way back into the contest before Samu Castillejo teed up Patrick Cutrone in the 83rd minute, with the former – who was sent off late on – also having a strong penalty shout during a frantic finish.
However, the result in Group F will lead to further speculation over Gattuso's position, with media reports suggesting Roberto Donadoni is being lined up as a replacement.
"We lost direction. In this game, we suffered," Gattuso told Sky Sport Italia .
"We are losing our belief, the team is not playing with a free mind and is suffering a lot.
"At this moment the mentality, the fragility of the team worries me. We must understand, at this time we are not even as good as we were for so long, we have not found that fluidity.
"We must talk to the players, see what problems there are, but my tactical ideas may be wrong too."
Gattuso's Milan have struggled defensively - they have not registered a clean sheet in Serie A so far this season – and, worryingly, looked short of ideas in attack until the closing stages against Betis.
"We must understand what is the solution to improve," he added.
"At a mental level we are not able to react, we are not masters of the field. In defensive transition we have always suffered, but we were creating an attack. We did not even do that."
Milan return to domestic action with a home game against Sampdoria on Sunday.