Alan Dickens described Saints as 'devastated' after victory was snatched from their grasp late in the day at Sandy Park.
Thomas Waldrom scored from the final play of the game and Joe Simmonds converted to secure a 31-30 victory for the Aviva Premiership champions.
Tries from Rob Horne, Ben Foden and Harry Mallinder had given Saints a deserved 30-17 lead with 10 minutes remaining.
But Don Armand's effort and Waldrom's dramatic score helped to claim a bonus-point success for the Chiefs.
And Saints interim head coach Dickens said: "I'm gutted for the players.
"We talked this morning at the hotel about having bags of energy and enthusiasm and battling for each other. We saw that.
"We're devastated in there in terms of coming out on the wrong side of the scoreboard.
"They got on the front foot in the last quarter, got field position, we gave away penalties and it gave them an opportunity to sneak it at the death, which they did.
"For whatever reason, they got into our third - and I'd question a couple of decisions for them getting there - but they're a champion side and they did it at our place before Christmas and got a bonus point. They did the same again today."
Referee Christophe Ridley, who is 24, was taking charge of his fourth Premiership game.
And Saints were disappointed with some of the decisions that went against them.
"You make your own luck, but the ref does help with that sometimes," Dickens said.
"It's a professional game and all of our professional refs are refereeing in the Six Nations."