His side scored only one try, relying in the main on the goal-kicking boot of Welsh international five-eighths Dan Biggar.
Northampton had been 19-0 up at halftime but let Lyon back into the game which saw former All Blacks prop Owen Franks and centre Matt Proctor make their club debuts off the bench late in the match.
Boyd said the damage had been done by halftime but it was a recurring theme that while achieving the win they were not happy with the performance.
"We're pretty disappointed with the second half but Rome wasn't built in a day, was it?
"Lyon are a really good side but with an ounce of luck we might have scored a couple more tries in the first half. We created a few and didn't quite finish them off," he said.
"Our execution and finishing aside, the way we controlled the game during the first half was pretty good.
"We didn't get possession and territory at the same time in the second half. We gave away a couple of penalties and there were some loose bits of skill execution," he told media after the game.
"When we kicked to make outside of 21 points up, we would have had to capitulate to lose at the that stage, but it wasn't great."
Boyd said he had seven players back from World Cup duties and also Franks and Proctor who hadn't been released from New Zealand until after the World Cup.
"They all want to play for the club and they realise that as senior players and leaders their contributions are really important," he said.
Northampton travel to Treviso to play Benetton in their next game.
In other games on Sunday, Connacht beat Montpellier 23-20 and Racing 92 beat beleaguered Saracens 30-10.