Looking back at the Premier League clash at White Hart Lane, Gallagher believes the decision to award a penalty against Rose, when he appeared to win the ball in a challenge with Edin Dzeko, was wrong.
However, he feels referee Andre Marriner had no choice but to dismiss the Spurs defender after pointing to the spot.
"It wasn't Andre's fault," Gallagher said. "Danny Rose has got so much of the ball. Dzeko's knees have buckled. For me, it's a good tackle.
"It's the assistant who gives the penalty, and unfortunately once the penalty's given, the argument is it's a red card, it's got to be a red card because it's denying a goal scoring opportunity, but for me, no. No penalty. No red card.
"The referee should just give a corner, he's played the ball out, but the assistant has come in and he's flagged. In all honesty, he's given what he thinks he's seen. But he's read it wrong, and unfortunately he's sold the referee down the river. It should be a corner, and we can't defend that."
Tottenham endured other misfortune during their 5-1 reverse at home when Michael Dawson ghosted in behind Emmanuel Adebayor to meet a free-kick and volley into the net from close range, only to be denied by the assistant's flag.
On this occasion, Gallagher backed the decision from the same assistant, on the basis that Adebayor was offside when he challenged City keeper Joe Hart for Christian Eriksen's aerial delivery.
Gallagher said: "It's the same assistant. And I think he's got this one 100% right because the law does say if a player attempts to challenge for the ball, he must be given offside. Adebayor's in an offside position as the ball comes in.
"Hart goes to play the ball and Adebayor goes to head the ball. Now the minute he goes to head the ball, he's interfered with an opponent and therefore he's guilty of an offside offence. Therefore the goal was correctly disallowed."
Across London, Chelsea endured a frustrating night when they were held to a scoreless draw by West Ham at Stamford Bridge.
Chelsea boss Jose Mourinho complained about time wasting from the Hammers, which resulted in seven minutes being added at the end of the match.
Mourinho also criticised referee Neil Swarbrick's decision to rule out a Samuel Eto'o effort when the striker put the ball in the net as West Ham keeper Adrian prepared to take a free-kick.
Gallacher said: "He's actually given a free kick. I just think when Neil gives the original decision, there's a little lack of clarity really, people are left wondering.
"But you see from the original offence when there's a clash with the goalkeeper in the six-yard area, (Swarbrick) goes to the goalkeeper, says free-kick and puts the ball down."