Stefano Pioli criticised the mentality of his fragile Inter side after they crashed out of Europe on Thursday, losing 3-2 at Hapoel Be-er Sheva having led 2-0.
Inter captain Mauro Icardi gave his side the lead in Israel after just 12 minutes and Marcelo Brozovic soon added a second to put Pioli's men completely in control of the Europa League tie.
But Lucio Maranhao struck back and when goalkeeper Samir Handanovic was sent off and conceded a penalty, Anthony Nwakaeme levelled from the spot before Ben Sahar scored Hapoel's dramatic late winner to dump Inter out.
Pioli felt Inter believed they had done enough to win the game and allowed the Israeli side to come back into the match by dropping their intensity.
"We stopped playing as a team and were presumptuous," Pioli told reporters. "That should never happen and we cannot afford to do that if we want to win games.
"We had the chance to go 3-0 up and didn't take it. We must work hard to ensure we don't keep giving away certain opportunities. We cannot play such a two-faced match. In the first half we did really well, badly in the second. All we needed to do was maintain that attitude."
The Italian said Inter's fitness could not be blamed for their collapse, with the Serie A side having conceded five times in his two matches in charge.
"In fitness terms we're ok, as we pushed at the end. What matters here is the mentality and we must improve," Pioli said.
"The past no longer counts, what matters is the present and we cannot be satisfied with our work. We are working on all fronts: physical, psychological and tactical. A team that plays that well in the first half cannot offer a second-half performance like that.
"Inter have players of great quality, but we need to know how to suffer under pressure. The performance was not worthy of Inter. We got too deep and allowed Hapoel back into the game. I changed a few things, trying to recover the balance that we had lost."
Hapoel coach Barak Bakhar accepted Handanovic's dismissal was a pivotal moment, but said his attacking changes helped his side to pull off a historic victory over the Serie A giants.
"In the first half we played badly, we were too fragile," Bakhar said. "Then in the second half we grew, helped by our fans.
"When we play against European teams we must be daring. For this reason I had to introduce offensive players to retrieve the result. Then obviously the game changed with the expulsion of Handanovic.
"Physically we were very good. The credit belongs to everyone, not just mine: the trainers, doctors and all the staff."