Down 8-25 during the first half, Northampton fought back with 24 unanswered points before claiming the win when first five-eighths Dan Biggar landed a penalty goal after a deliberate knock on was ruled against Benetton.
Boyd told media after the game, "I don't think either side would sit there and say they played well enough to come away with five points.
"We did well to come back into it and the try before halftime was crucial obviously because going in 25-8 down at halftime might have been a bridge too far.
"We were just so far off our game, despite the fact we talked about how tough it was to play here and how well they've performed here.
"We were just miles off our game, which was really disappointing, and it was probably our worst effort of the year," he said.
Boyd said the halftime message had been that Northampton only had to score twice to get level and with 40 minutes to do that there was no need to rush.
"The positive is that we found a way to win, but we were far from in control.
"We were loose and sloppy – all the things we talk about not being, we were.
"It's the challenge of the human mind. We've had some patches in the past few weeks where we've been clinically really good, but today we were sloppy," he said.
Northampton next face a double-header against Leinster in December.
New Wallabies coach Dave Rennie's Glasgow team were unable to repeat their first round success when going down 18-34 to Exeter.
Glasgow led 13-10 at halftime but two minutes into the second half the England Test pairing of Jack Nowell and Henry Slade combined to score to claim the lead.
Glasgow's next game is at La Rochelle on December 7.
In the Challenge Cup section former All Black and Chiefs flanker Liam Messam scored a key last minute try which, when converted, resulted in Toulon beating Brad Mooar's Scarlets side 17-16.
Pat Lam's Bristol side set themselves up to top their pool when securing a 36-0 win over Brive. Lam said afterwards, "It's a big statement from the boys, winning in France is never easy and it was a team effort."
Other results over the weekend were: Ulster 18 Clermont Auvergne 13, Saracens 44 Ospreys 3, Toulouse 32 Connacht 17, Leinster 13 Lyon 6, Munster 21 Racing 21, Harlequins 15 Bath 9.
In the Challenge Cup, Newport Dragons beat Enisei-STM 49-22, Bristol beat Brive 36-0, Paul beat Calvisano 61-10, Edinburgh 16 Bordeaux Begles 16, Toulon 17 Scarlets 16, Castres 17 Worcester 9, Stade Francais 13 Zebre 12, London Irish 45 Bayonne 31, Wasps 32 Agen 14.