Mauricio Pochettino says his players took their foot off the gas at 3-0 in their 3-1 victory over Southampton on Wednesday, allowing their visitors a late flourish at Wembley.
Harry Kane, Lucas Moura and Son Heung-min all scored inside 55 minutes to put Spurs firmly in control, with new Saints boss Ralph Hasenhuttl watching from the stands.
But the visitors were not without their own chances and hit the woodwork three times, as well as drawing a superb double save from Hugo Lloris before Charlie Austin netted a late consolation.
"I think it was an important three points," said Pochettino, whose side were beaten 4-2 by Arsenal in the north London derby on Sunday.
"Tough evening, not easy to play after the week we've had and I'm so happy because we are back in the top four places.
"It was a strange game, when it went to 3-0 and maybe we started to think the game was over and of course maybe Lloris was Man of the Match because he made good saves.
"It was difficult to play in three emotional games in the past week [including a 1-0 Champions League win against Inter] and you feel it in your legs but we kept going, 33 points and back into third in the table.
"Of course it was a difficult evening for the players but also for the fans and sometimes we need to find the motivation."