Stuart Beavon's second-half red card offered Barnet a lifeline but Gallacher scored twice more to complete his hat-trick before Garner completed the rout eight minutes from time.
"We didn't want to be one of that team that was in the Sunday papers after an upset," he said. "We worked hard and gave them the respect they deserved.
"We knew they could be play and could play from the back and we had to stop them getting into their rhythm.
"He (Gallacher) has come from a higher level and we know he can score and is a different class on the ball. Hopefully he can do it for us for most of the season now. It will give him a great lift.
"We are here to get promotion and we set high standards and that's what we want the players to follow.
"They are all playing for the shirt and all wanted to play. When they out there know they need to keep the shirt because if they don't perform there is someone out there waiting to grab it."
- Sports & Recreation
- Joe Garner