The black, green and gold concluded their campaign with a 30-24 Gallagher Premiership loss at The Rec after giving their all.
Two tries from Taqele Naiyaravoro, on his 50th Saints appearance, a sublime effort from Rory Hutchinson and a tidy finish from James Grayson had put the away side ahead.
But Bath came roaring back and eventually sealed the win thanks to a Josh Bayliss breakaway try, moments after it looked like Saints should have been awarded a scrum penalty that could have won them the game.
"We're probably more disappointed than last week (the 29-26 defeat to Exeter) because I didn't think we played as well," Boyd said.
"Average games of rugby come down to critical moments and those critical moments can be decided by your own players, their players or the referee (Ian Tempest) and I thought we were on the wrong end of a couple of decisions that might have made a difference, but we didn't get the result.
"It's a tricky game emotionally for the boys.
"We had a short turnaround and we thought we'd locked in about what was important for us around consistency, finishing well and stuff like that.
"But at the end of the day, we went away from script in the first 15, 20 minutes and took a while to settle down.
"We didn't get it quite right and then played some pretty good footy in the last bit of the first half.
"We knew exactly what we needed to do - I thought they were out on their feet at the end of the first half - but we weren't able to control the ball and we let them slow it down and grind away.
"Near the end there when it was pretty close we were on the end of a few decisions that might have made a difference."
On the possible scrum penalty two minutes from time, Boyd added: "I just don't think he was particularly keen on giving that penalty - it was a clear penalty.
"He said the ball came out, but what will be, will be."