The black, green and gold headed in at half-time level at 6-6, having enjoyed plenty of territory and possession.
But Saracens eventually cruised home, scoring three tries in the second period as they strengthened their grip on second place in the Gallagher Premiership.
Saints have now suffered four successive defeats in all competitions and have slipped from third to sixth in the league standings.
And when asked what he thought of the showing against Saracens, boss Boyd said: "We certainly felt at half-time that we'd had plenty of opportunities and we didn't convert them.
"It was partially down to us and partially down to the fact they've got a very good defensive system and process.
"We talked at half-time about the fact there would be four or five moments in the second half that would decide the game but unfortunately they got three bits of territory and three tries.
"We had a long period (in the first half) where we could have taken the three but I just felt we put too much into it to come away with three points and if we were going to go on and win, we needed to get a seven out of that.
"We were a little bit grumpy about a scrum penalty where there was a clear hinge and he just went to the ground so we had all that effort and it was undone by a refereeing decision to give them a penalty when pretty much most of the game their scrum was under pressure.
"We lost the kicking battle too many times and the rain didn't help us. It was greasy and hard to run and they want you to make a poor decision or mistake at the wrong end of the field.
"We got trapped into playing that aerial ping-pong game, which I don't particularly enjoy, but sometimes you have to stick with it otherwise you get yourself into trouble.
"We've got to reflect on the balance of our run-kick game."