A second-half brace from Dan Scarbrough hauled Saracens back into the match but Bath, who led 28-18 at the interval, held out with Gaffney blaming lacklustre tackling for the defeat.
"We made more than our fair share of mistakes and lost the game. You can't gift that many tries and stay in the game," he said.
"We haven't conceded that many points in any game this season, or conceded four tries either.
"Our defence is the second or third best in the Premiership so to do what we did in the first half was abysmal.
"We put ourselves under enormous pressure. The amount of ball we controlled in the first half was minimal and we didn't play the game we wanted.
"This result is extremely disappointing as far as we're concerned. We set ourselves the goal of winning this competition.
"We were in a position to do that but we didn't play the way we wanted and made some schoolboy errors and you can't do that against Premiership side.
"We improved in the second half but the horse had bolted. We got the result we deserved."
Seven places separate Bath and Saracens in the Guinness Premiership but the London club's suicidal first half saw the form book ripped up.
The Challenge Cup is Bath's last remaining chance of winning any silverware this season and Bath head coach Steve Meehan felt excellent team spirit underpinned Sunday's victory.
"I don't think it was the best 80 minutes but it was one filled with commitment," he said.
"We've probably played with more commitment than we've seen in the past. It was a show of desire at wanting to be in the final.
"Saracens executed very, very well and put us under a lot of pressure but the guys scrambled and worked hard for each other.
"It was one of those games where defence wins you matches, but we were quite positive in attack as well.
"The first half in attack things worked out nice for us, particularly the last play in the first half when Berne scored. That was something we've been working on."