Garner appeared to swing and miss at Brentford’s Sam Samuels right in front of the technical area.
A brawl ensued as tempers flared.
After deliberating with the fourth official and his assistant, referee David Webb decided to book Garner.
But Gallagher said it was not a yellow card incident.
He said: “Teams come to Deepdale, they know about Joe and they try and rough him up. We try and protect him.
“I don’t think he deserved the yellow card.
“One of their lads has run 10 yards and got into him. Joe is feisty and fiery and he has jumped up himself.
“The ref said Joe has jumped up in an angry manner but players are coming from a long distance to get involved with him.
“Joe works hard and wears his heart on his sleeve.
“Teams see what he did last season, all the goals he has scored – he is a menace, he roughs people up but he will give it and take it.
“I think their big centre-half had one eye on Joe and wasn’t really concentrating on the ball and kept blocking him every time he was going for the ball.
“Joe is experienced, he has matured a lot.
“Sometimes you have to have a quiet word with him because he is feisty but we will dust ourselves down and now we have eight days to prepare for our next game against Derby.”
Jake Bidwell opened the scoring in the 22nd minute with a curling free-kick that got a touch off Greg Cunningham as it flew past a sea of bodies and static PNE keeper Sam Johnstone into the back of the net.
The Lilywhites replied immediately as Adam Reach slotted the ball home.
But just before half-time, Alan Judge latched on to defender Yoann Barbet’s sublime cross-field ball and outfoxed Cunningham to slot home.
North End peppered Brentford’s goal in the second half and Gallagher believes Garner’s tap-in was incorrectly ruled offside.
But John Swift killed the game off in the 80th minute as his deflected strike looped over Johnstone.
Gallagher said: “It was a bad day at the office.
“In the first half we were five yards off the pace and if you give players like Judge and Swift time on the ball they can hurt you.
“It took them to score to give us a kick up the backside.
“We weren’t playing well but we managed to score. We should have put more pressure on the ball for Judge’s goal.
“In the second half there was a lot more passion, a lot more energy.
“We left ourselves a bit open for the counter-attack but we were trying to get back in the game. We put the ball in the box and asked questions.
“Eoin Doyle had a good chance just after half-time and I think if we had got that it would have been a different story.
“But we have to give credit to their keeper David Button He made two fantastic saves.
“I don’t know how he has saved the one from Joe and I was told that the goal Joe scored was not offside. It just didn’t go for us.”