Bentancur only recently returned from an eight-month lay-off because of a serious knee injury and was making his first start but was injured in the 26th minute by a poor-looking Matty Cash tackle.
"I was disappointed to lose him (Bentancur) because he started the game so well, you can see his quality, and that's a reason we got such a foothold in the game," Spurs manager Ange Postecoglou said.
"With him coming back from a serious injury, you are concerned about it.
"From what I understand, it's his ankle rather than his knee, but it's not what we need right now, another injury, but that's what we're going through."
Early Premier League pacesetters Tottenham have now lost three successive league games and face several more weeks without key players after slipping out of the top four.
The club's England forward James Maddison (knee) and Netherlands' central defender Micky van de Ven (hamstring) both suffered long-term injuries against Chelsea this month, while Brazil striker Richarlison has had surgery on his pelvis.
Ivan Perisic, Manor Solomon and Ryan Sessegnon are also sidelined, while Spurs' Argentina centre-back Cristian Romero has one more game of a three-match suspension still to run.
Injuries and suspensions have thrown a spanner in what was Tottenham's best start to a top-flight season since 1960.
"We have got eight (injuries), Bentancur nine, we had a couple of suspensions today and we've only got a squad of 25," Postecoglou told reporters.
"You do the sums and that's what we've got. We lost Ashley Phillips during the week as well."
England Under-19 defender Phillips was Spurs' sixth signing under Postecoglou in the last transfer window when he joined from Blackburn Rovers for two million pounds.
"It is just the situation we're in at the moment, but we'll get through it," he added.
"It might take a little while but we'll get through it and as long as we show the same intent and play the football we did today, I've got no doubt when we come out the other side, we'll be a very good football team."
