The home side had Api Ratuniyarawa sent off 30 minutes from time and conceded a try in closing stages as Irish snatched a Gallagher Premiership win at a stunned Gardens.
Saints had led 13-8 in a scrappy game, but Ratuniyarawa's sending off eventually proved key as Irish scored twice in the final seven minutes to win it.
It ended their seven-match losing streak and brought a conclusion to Saints' four-game winning run.
And Boyd said: "The barometer swung past frustration to anger.
"Credit to Irish, they came with a plan and executed it pretty well. They especially defended well at times.
"We were the masters of our own demise both in our skill execution and the fact we didn't win collisions when we needed to.
"We weren't very disciplined at times.
"We were two minutes away from stealing a game that would have been unjust either to win or lose really."
The Saints supporters were furious with referee Tom Foley, who only showed a yellow card to Irish scrum-half Ben Meehan for an off-the-ball tip tackle on Cobus Reinach.
And the boos grew louder when Ratuniyarawa was dismissed for a shoulder charge that the referee and TMO felt made contact with Harry Elrington's head at a ruck.
And when asked about Ratuniyarawa's red card, Boyd said: "The best thing I can do is say no comment.
"It was a big turning point and I thought their yellow card, the body slam after the whistle, was a pretty interesting decision so I'll say no comment to that as well."