The England forward went down after 55 minutes and was unable to continue despite extensive treatment and was replaced by Seamus Coleman.
The positive news is that he was able to walk off unaided, but speaking after the game assistant boss Duncan Ferguson admitted the injury was “a worry”.
“Dom is our main striker and he scored another good goal tonight.
“We will miss him if he’s not going to play but the boys showed good spirit when he went off the pitch and scored two goals.”
When asked about the extent of the injury, Ferguson added:
“We’re not quite sure [yet],”
“He was complaining about his hamstring when he came off the pitch. We’ve not got an assessment but it does look like a wee bit of a hamstring tweak.
“That’s football. He’s a great wee player, he comes on and makes a great impact and scores the winner so a great moment for him.”
It means Calvert-Lewin must be considered a doubt for Sunday’s visit of Fulham, though Everton will be hoping the issue isn’t serious enough to rule him out of next week’s games against Manchester City and Liverpool FC.
If he does miss out then Josh King is likely to be handed his first Toffees start.
The Norway forward has made two substitute appearances for Everton since joining on loan from Bournemouth but was cup-tied for the Tottenham game.
On the plus side, midfielder Allan is expected to be in contention to return against the Cottagers.
The Brazilian returned to training this week after six weeks out with a hamstring injury of his own.