The black, green and gold were beaten 32-9 on their return to Aviva Premiership action.
Saints had bossed the opening stages of the game, going 6-0 up thanks to two Piers Francis penalties.
But they were eventually overwhelmed, with Bath bagging three tries on their way to a comfortable victory.
And scrum-half Reinach, who started the game, said: "We just couldn't finish the chances off in the first half.
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"We'll have to go back to the drawing board and look at how we do stuff.
"We've got to tweak it because we're not far off.
"One tweak here and there and we'll be dominating, breaking lines and scoring tries.
"I don't think the scoreline reflected what we did on the pitch on Friday.
"The boys played hard and we were in it for 60 minutes.
"At 19-9, one score and we were in the game.
"I definitely don't think the scoreline reflects what we were trying to do.
"Unfortunately, the scoreline was bad and we now need to regroup and take on London Irish on Saturday."