Spurs fought back from a goal down to claim a 6-2 victory at Goodison Park, with Alli and Christian Eriksen scoring once and Harry Kane and Son Heung-min each netting a double.
The result lifts Pochettino's men to within two points of second-placed Manchester City, but their victory was soured when Alli failed to emerge for the second half following a heavy challenge from Everton goalkeeper Jordan Pickford just before the break.
"He didn't feel a big problem," the Spurs boss told Sky Sports.
"Maybe [he was] a little bit tired from Wednesday. I hope it's not a big issue. It was a precaution."
Pochettino added at a news conference: "I didn't see [the challenge]. I am curious to see the action.
"I didn't want to say because I've not seen the video. It was a tough action. We hope it's not a big issue."
They then take on Tranmere Rovers in the FA Cup third round three days later.