The Liverpool defender received a yellow card for a foul on Amadou Onana in the second half of the Goodison Park clash.
However, Everton manager Frank Lampard felt that van Dijk should have been given his marching orders for the tackle - and VAR should have looked at the incident.
But former Premier League official Gallagher reckons on-field referee Anthony Taylor got his decision correct.
Gallagher told Sky Sports: “I think yellow card. He goes down, I get that, but the maximum impact comes on top of the foot.
“Because he’s come a short distance, he hasn’t got the speed and intensity.
“He goes down, he catches him but the big impact is on the bottom of the foot. I didn’t say it wasn’t a foul, I think it’s a foul and a yellow card.”
Everton were denied a victory when Conor Coady’s 69th-minute goal was adjudged offside following a VAR review.
Replays showed that Liverpool’s James Milner may have got a slight deflection on Neal Maupay’s cross and debate has raged with the goal should have instead stood.
Gallagher feels the laws of the game render that argument irrelevant, however.
He said: “Whether it hits his foot or not it is immaterial. The law says he has to deliberately play the ball or be in possession of the ball.
“That’s an attempted block and deflects into his path. However you cut it, the law is quite clear; in that situation, if the ball strikes his foot, it’s a deflection and it deflects to Coady.
“He has to be in possession of the ball, have control of the ball or deliberately try to play that ball safely.
“His sole intention is to block that cross. It flies off his boot, no doubt about it, but that’s negated.”