Tottenham arrived in Milan with a 3-0 lead over Inter, but they conceded four goals, with their passage to the last eight of the Europa League only secured thanks to Emmanuel Adebayor's away goal in extra-time.
Slack marking allowed Antonio Cassano and Rodrigo Palacio to score either side of the break and Gallas mis-judged a free-kick to stab in to his own goal before Ricardo Alvarez took advantage of some statuesque defending for Inter's fourth in extra-time.
Andre Villas-Boas appeared to have banished the defensive jitters that had blighted the opening third of Tottenham's campaign, but their back four has looked weak in the last two games, which have seen the team concede seven goals.
Spurs' top four hopes will be in severe doubt if they continue to leak goals in their final nine Barclays Premier League games, but Gallas is sure the defence will tighten up quickly - starting with Sunday's home clash against Fulham.
"In the next game it won't happen," the Tottenham defender said.
"It won't happen because all the players know what they have to do.
"Against Inter we didn't play well. It was not good and all the boys know we have to react."