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."
It was not just the 11 players on the pitch who were nervous on Thursday night. The 2,000 travelling fans were also forced to bite their nails throughout as Spurs seemed intent on throwing away a tie that seemed almost impossible to lose at kick-off.
The Spurs faithful will no doubt be worried that this is the start of a similar decline to the one that their team suffered last year.
The Londoners, then under Harry Redknapp, led Arsenal by 10 points in February, but they threw away the advantage thanks to a poor run in the final quarter of the season.
Gallas insists the same will be no repeat this term.
"It won't happen," the Frenchman said. "We know we have a great chance to qualify for the Champions League and we know that we can go very far in the Europa League.
"Sometimes you can have bad moments and maybe at home we are in a bad moment, but we know what we want at the end of the season and everyone will be ready for Sunday.
"I think the manager will have a meeting with us on Saturday to say what was wrong and correct what wasn't good. It is very important.
"To concede seven goals in two games is not very good. It can mean some things are not well. It was not the real Tottenham against Inter, but we can move on."
Tottenham dodged a long trip to Rubin Kazan, and potentially difficult ties against Chelsea or Benfica by drawing Swiss champions FC Basel in the quarter-finals.
Thursday night's performance has meant Spurs are now second favourites behind Villas-Boas' old club Chelsea in the running for the tournament.
Spurs striker Jermain Defoe admits the performance in Italy was not acceptable, but he insists the team are still confident of making the final in Amsterdam and lifting the trophy.
"We're disappointed as professionals," he said. "Even though we're through, we're not happy at losing like that.
"But we still don't have to take any steps to join the top sides because in the first leg we were so much better than them.
"There could have been a lot more goals at White Hart Lane.
"Last night [Thursday night] was difficult, but we have done so well all season and we don't want to let it slip."