With the in-form South Korean Son Heung-min playing his last match before heading off to the Asia Cup, the last thing Pochettino needed was the sight of Kane hobbling off the pitch after being clattered by United's Phil Jones late on.
Kane and Son have scored 22 goals between them this season and, without them, Tottenham look short of goals, especially with Spaniard Fernando Llorente struggling for form.
"It was a clear foul on Harry Kane, a big hit, (referee) Mike Dean said he didn't see it," Pochettino said of Jones' challenge.
"Kane twisted his ankle and we hope that it is not a big issue. My worry is that it was a bad tackle in the last moment.
"It wasn't the intention of the United player but it was a bad tackle and now he has bit of a swelling on his ankle and he was limping after the game.
"We are going to lose Son for the Asia Cup and if Harry Kane suffers an injury, it is going to be massive for us."
Tottenham also lost midfield powerhouse Moussa Sissoko to a groin injury before halftime, adding to their woes.
Defeat left Spurs nine points behind Premier League leaders Liverpool and they will be five behind Manchester City if the champions win against Wolverhampton Wanderers on Monday.
(Reporting by Martyn Herman; Editing by Ian Chadband)
