Boro took a first-half lead through Simon Heslop's 20-yard strike but found themselves behind just after the break.
Francois Zoko made it 2-2, only for John Mousinho to give the Gills all three points 14 minutes from time.
"I think we were fortunate to be ahead at half-time. I thought we were lacklustre," said Westley. "The players looked tired and fatigued and there are no excuses for it."
He added: "After nights like these you're tempted to ring the changes for the next game. You've got to take the season in stages.
"We had five points after 10 games, I think, and we've bounced back from that. On the whole, we're on a better run of form but it's difficult when you know about the depth of our squad. I think that's been an issue for us.
"Over those 90 minutes, they didn't deserve to win and I don't think we deserved to. In these circumstances, one side gets lucky and so you can't have any complaints."
- Sports & Recreation
- Simon Heslop
- John Mousinho