Hoyte's evening was ended early after his challenge on Roarie Deacon earned him a red card, with Taylor dismayed that Boro goalkeeper Chris Day did not suffer a similar fate earlier in the game.
Day brought down Cody McDonald in the box which set up Luke Norris's winning penalty but Taylor is adamant the keeper should have seen red.
"The referee told me he didn't think Cody would have got to the ball," he said. "I'm startled with that decision too.
"We've had a red card for something that happened 40 yards away from goal and we get a penalty where the last player brings my player down and got a yellow card.
"I didn't agree with &£91;Hoyte's red&£93;. I'm going to look at it. I can't for the life of me see where it's a red card. If we think it's the wrong decision, we can appeal.
"It was a very tough match, you expect that. I thought we did some very good things, especially in the first half, and we deserved to win.
"The work-rate the players put in was fantastic. They hung in there when we went down to 10 men."
Day was lucky to escape punishment for an early tangle with Norris and was booked for bringing down McDonald in the box soon after.
Norris stepped up to break the deadlock from the spot and came close to adding a second but his shot was well saved by Day.
But Hoyte's lunge on Deacon in the 63rd minute put a sour note on the successful evening for the Gills.
Boro manager Graham Westley admits his side were too defensive throughout the game, preferring to keep possession than create chances.
"I never get excited about performances when we've lost the game - I don't believe in that," he said.
"What you have to say is that the team was much better than when we played here against Wycombe.
"We played far more patiently which showed development in our game. We need to get the balance right between driving forward without too much intelligence and being too patient with our play and not opening sides up.
"We don't think we gave ourselves enough opportunities in the game and we didn't take our chances in the final third when they did come.
"Quite often we saw ourselves getting into the final third and then working our way out - keeping possession rather than taking shots.
"We showed with our possession and shots on goal that we did our best to work the football and be constructive."