Frank's side were on course to take a point off the title challengers after Yoane Wissa found the net in first-half stoppage time to cancel out Declan Rice's 19th-minute opener.
However, like November's reverse fixture, Havertz scored a late winner to leave Brentford with nothing to show for their efforts.
Frank believes the Germany international was fortunate to still be on the pitch after being accused of diving in the box under a challenge from Nathan Collins.
Havertz, who was already on a booking, appeared to go to ground in anticipation of contact from the Brentford defender, who dangled his right leg towards the Arsenal attacker.
The Brentford players appealed for a second yellow card towards referee Rob Jones, but Havertz escaped punishment for what Frank labelled a "clear dive".
"I actually think, and I would never normally do this, but I think Havertz shouldn't be on the pitch when he scored the goal," Frank said in an interview with Sky Sports after Saturday's game.
"For me, it was a clear dive - the penalty shout. If you see that slowly back, it's clear. Maybe, it's difficult for Rob the ref but the linesman should have seen it, in my opinion, clearly."
The Brentford head coach also provided an update on captain Christian Norgaard, who was forced off in the first half at the Emirates.
"It was a contact injury," Frank told the club's official channels. "Hopefully, fingers crossed, he'll be available for Burnley."
Frank will nervously wait to find out the extent of Norgaard's injury, with the Bees already having to cope with a lengthy injury list which includes Josh Dasilva, Rico Henry, Ben Mee, Aaron Hickey, Ethan Pinnock, Kevin Schade and Bryan Mbeumo.
Tottenham Hotspur loanee Sergio Reguilon was omitted from Saturday's matchday squad, but Frank is confident he will make a swift return to action.
"Sergio has a minor hamstring injury," The Brentford boss added. "He should be available for Burnley."
Having taken just one point from their last five matches, the Bees are sitting in 15th place in the Premier League table, with five points separating them from the drop zone.