The Rossoneri suffered their third defeat in four Europa League matches this season, losing at San Siro after Ferencváros capitalised on defensive errors to claim all three points.
AC Milan struggled to impose themselves on the contest, with the visitors making the most of their opportunities while the home side failed to find a convincing response.
Bartesaghi acknowledged that the team's approach had not been good enough and said they needed to react more quickly when things began to go wrong.
"We were missing the attitude from the start. We should have reacted in the moment instead of waiting to take a few blows," he told Sky Sport 24.
The defender felt Milan had allowed Ferencváros to create chances through their own mistakes, rather than making the visitors work to find openings.
"They created chances from our errors. From tomorrow we'll lick our wounds and look at what was done wrong, then approach the next match with the right determination and a different team spirit."
The result represents another setback for Milan's European campaign, with the team having now lost three of their four matches in the competition.
Bartesaghi's comments reflected the frustration inside the dressing room, but also the need for an immediate response. He called for the players to examine their mistakes and approach the next fixture with greater collective commitment.
Milan will have little time to dwell on the defeat, with their attention turning towards their next domestic assignment. Bartesaghi made clear that the team must learn from the performance rather than allow another disappointing result to affect their confidence.