Heathcote, 20, who kicked four conversions and a penalty, is understudy to All Black Stephen Donald and still an academy player, although he has recently signed a three-year deal with the club.
Donald is currently ruled out by a knee ligament injury and may not be back until early April, but Davis warned that he is not going to walk back into the team.
"Stephen's going to have to fight his way back into that number 10 shirt," Davis said. "The guy who's there at the moment is going from strength to strength and learning the game.
"The crowd here at the Rec know their stuff and when Tommy's on the ball they get excited about what he does for the team. He's a level-headed guy but he was terrific again.
"He's a good player. He has the skills, the passing game, the kicking game, but he's brave too in the way he takes the line on and also in defence. But he's got his feet on the ground and he's a terrific guy to work with."
Davis was just as happy with the rest of the performance, which featured tries by Tom Biggs (two), Michael Claassens (two) and Matt Banahan.
"We took them apart physically. We're evolving strongly as a unit now," Davis added.
Wings Tom Arscott and Miles Benjamin crossed for Worcester, leaving head coach Richard Hill to reflect that it was "one game too far" after their heroics against Saracens the week before.
Hill said: "The danger after Saracens was that we might think that the job was done.
"We started brightly but we just ran out of steam a little. We lost a bit of intensity. The mind was willing so I couldn't really fault anyone for effort."
The former Recreation Ground favourite added: "Bath are one of the top three teams on form at the moment.
"It was good to secure the second try, we had a little bit of consolation there, but for some reason our set piece didn't function as it usually does.
"We've had a really tough, intense period since Christmas and the tank's a little bit drained."
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