The result, which followed a victory against Wolves, lifted Spurs a point clear of West Ham and renewed belief in their bid to avoid relegation.
Gallagher scored his first goal for the club since joining from Atletico Madrid in January and highlighted De Zerbi's individual approach as a key factor behind the improvement.
"The gaffer has been brilliant with us. He has brought the team together," Gallagher said.
"He has really worked on players individually with one-to-one meetings and one-to-one chats, trying to get that belief and confidence back in the players.
"He has done that with me and it has made a big difference. I know he has done that with a lot of the other lads."
Gallagher added that the manager's influence extends beyond individual conversations, with changes on the training ground and in team meetings helping to align the squad.
"As a team as well, all the work he has done on the training pitch and the meeting rooms, it has been fantastic and everyone is on the same page," he said.
The midfielder also revealed De Zerbi has encouraged him to rediscover the form he showed earlier in his career, particularly during a standout season at Chelsea.
Despite consecutive wins, Gallagher stressed that Tottenham remain focused on the task ahead, with a home match against Leeds United next on the schedule.
"There is a lot of work to do," he said. "We are fully focused on the next game, hopefully do the same performance and another win."
