A Clive Platt goal after a blunder by goalkeeper Jake Cole was all that separated the two sides at Sixfields, where Northampton made it an impressive nine home victories in ten outings.
But Cobblers had to work hard to secure all three points against a Plymouth side who did more than enough to have taken a share of the spoils in their bid to stay clear of the relegation zone.
Boothroyd said: "We didn't play anywhere near as well as we can but it's all about winning at this stage of the season. If you had offered me a scrappy 1-0 win before the game I'd have taken it.
"Most of my players were below par but we ground out the result although were a bit fortunate with the goal, but I'm pleased we kept a clean sheet.
"We didn't have a lot of luck at Wimbledon in midweek so it's evened itself out with the goal which won it. But we had more chances to make sure late on in the game and normally we would have taken them.
"Our run-in away is against teams around us and in the top half of the table and our home games are against teams in the bottom half. But that doesn't mean you are going to easily win all your home games so we must not be complacent.
"Plymouth made us work very hard, we had to scrap for the win. A year ago we were in their position and if they keep playing like that I'm sure they can get out of it.
"It will be just as hard against Bristol Rovers on Tuesday. It's all about making sure we are in the automatic places or the play-offs with four or five games to go."