Five second-half goals - including a hat-trick from Fernando Llorente - eventually ensured that Spurs eased through to the quarter-finals, but the game was marred by a number of controversial calls during the first half.
Erik Lamela had a goal chalked off for a foul by Llorente - despite the general feeling being that any infringement was not "clear and obvious" - while Spurs earned a penalty for a foul on Kieran Trippier which started outside of the box.
However, while acknowledging that decisions using the technology are taking too long, Gallagher has insisted that the correct calls were eventually made.
Gallagher told Sky Sports News: "VAR got all the big decisions right at Wembley, although he conceded the several minutes taken to verify the decisions on video would need to be shortened. Whatever time it took, everyone wants it faster. At the end of the day, the decisions were correct and the reason we wanted VAR was to get correct decisions.
"People are now moaning because it's got the decisions correct - alright, it will take a little bit of time to get it quicker, we want it quicker, but the right decision has come on the night.
"At the moment, people say they wanted VAR, it's now been put in place but people are saying it's got this and that fault. Let's iron out the little things we've not quite got right at the moment, get it quicker and smoother and get everyone embracing it."