Kane, 27, needed treatment on his left ankle after landing awkwardly following a challenge with Jordan Henderson.
The England captain also hurt his right ankle in an earlier challenge with Liverpool midfielder Thiago Alcantara.
The striker, who has a history of ankle issues, continued before being replaced by Erik Lamela at half-time.
“The second injury was worse than the first one,” said Mourinho. “He was coping with one but couldn’t cope with both.
“For Harry to leave a game when the team is losing is not a nothing injury.
“There are some players you can’t replace. When it happens it happens, but I believe we have to fight against it, we cannot do anything else.”
Kane has spent considerable time on the sidelines with a number of serious ankle injuries in recent seasons.
The striker was ruled out for two significant spells in the second half of the 2018-19 season, missing seven games when he damaged ligaments in his left ankle in January 2019 and then nine more matches with a lateral ligament injury sustained in April.
In 2017-18 he missed a month with a similar injury to the right ankle, and endured separate absences of six and four weeks during the 2016-17 campaign.
“You just hope it’s not going to be ligament damage that will put him out for a long time because he’s been absolutely phenomenal this season – his contributions, his passing, goals and assists,” said former Spurs defender Stephen Kelly on BBC Radio 5 Live.
“He’s been the all-round complete forward and unplayable at times. Tottenham just can’t afford to lose him.”
