Mirallas was restored to Everton's starting line-up for Sunday's game at Goodison Park after missing the previous four matches due to a hamstring problem.
However, the Belgium international was forced off at half-time and Moyes is now waiting to learn the full extent of the latest complaint.
"We don't think he has done his hamstring, he just felt it had tightened up," said Moyes.
"I don't think it is bad but the last thing you want to see is the recurrence of a hamstring injury.
"You can see what he offered us in the first half, something which we have probably missed."
Nikica Jelavic scored an injury-time winner against Spurs following Steven Pienaar's 90th minute equaliser and Moyes was pleased for the Croatian striker after a month without a goal.
The Everton boss added: "There were signs he was getting a little bit better but he looked a bit frustrated because we weren't getting the ball to him enough.
"But if he can keep getting the goals, and with Steven getting one, it keeps us moving along nicely."
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