Dean has been under the spotlight after overseeing two big decisions in Newcastle United's last gasp 2-1 defeat to Wolves on Sunday evening.
Magpies boss Rafa Benitez appeared furious in his post-match press conference in which he demanded VAR was implemented into the Premier League right this instant.
As a part of Sky Sports News' Refs Watch, Gallagher, alongside former Everton striker Kevin Campbell, analysed the major referee talking points from over the weekend.
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On the decision to send DeAndre Yedlin off in the 57th minute following a tussle with Diogo Jota, Gallagher passionately stated Dean made the correct call - and the inclusion of VAR would not have impacted the incident.
"Mike Dean - top drawer performance," said Gallagher, who retired in 2007.
"I would say he got all the big decision correct - 100% red card. VAR would have endorsed this red card as well.
When asked if Jamaal Lascelles could have got across to cover, Gallagher said: "Everybody has said that to me. The law says he has to be able to get a shot away at goal.
"He's got the ball under control, he takes one step forward, bang and he can shoot before the defender can challenge him."
Campbell, a player at Wolves' Black Country rivals West Bromwich Albion, countered Gallagher's argument - interestingly analysing that Jota had actually fouled Yedlin first.
He said: "I thought Yedlin was fouled. He (Jota) put his arm on him.
"Yedlin was ahead of Jota but when Jota checked him, that's how he got ahead - he pulled him back and then got ahead of him.
When asked if VAR would have spotted a potential foul on Yedlin, Gallagher stated: "I don't think it would - it's not and obvious error by the referee - it's a subjective decision on whether the referee feels he has fouled him or not.
"There is certainly physical contact but I thought he was alright to let him go. That said, the big decision is whether it's a red card and for me it's a 100% red card."
While Campbell disagreed with Gallagher on the first incident, the pair were in full agreement over Ayoze Perez's blow to the head.
Benitez wanted to see a red card for Willy Boly as well as a penalty kick awarded, nine minutes from times.
Gallagher believes Boly had zero intent to hurt Perez while Campbell says putting your head in where it hurts is part and parcel of being a striker.
"I think he (Dean) thinks Boly used his arms for leverage and not as a weapon," Gallagher said.
"All players raise their arms to come off the ground - you see that and I thought the ball had hit him in the face.
"I don't think he throws his elbow - I think his elbow's always there because he challenges for the ball and connects with him.
"VAR would have fully endorsed what Mike Dean, it's exactly the same. We've both seen the same video and think the same."
Campbell agreed: "As a striker, it's a tough one because the defender can't actually see him. He's a big guy (Boly) so he's using his arms and unfortunately catches Perez."