The hosts led 15-5 at half time but were forced to withstand a tremendous second-half fightback from the Chiefs, who failed to even pick up a losing bonus point for their efforts due to a late missed penalty.
Tries from Ben Williams, Kyle Eastmond, who both crossed before the break, and Francois Louw proved enough for Bath, even though they had Dan Hipkiss red-carded with seven minutes to play in a see-saw contest.
"I'm very proud of the character we showed but not so much of certain aspects of the way we played in the second half, such as the penalty count," Gold said.
"We'll take that win against a team of that quality though. We've got massive respect for Exeter. They're one of the toughest opponents we've played this season."
Opposite number Rob Baxter was left to lament a poor first-half performance but was not blaming the rigours of two weekends of Heineken Cup action.
"My frustration is not about coming up short - it's with that first half performance. We just lacked a bit of clean decision making," Baxter said. "We also missed a few kicks at goal. We wouldn't have been talking about losing bonus points then (had we scored them).
"In the second half we looked great and full of energy. I've got to be pleased with the guys' physical endeavour but we found ourselves two tries down without firing a shot.
"It's disappointing that we came away without even a losing bonus point."
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