Town lost via Steve Elliott’s 45th-minute goal but remain third in the npower League Two table after Burton Albion were held to a draw by Accrington.
Boothroyd’s men had a number of chances to equalise in the second half with Chris Hackett in particular enjoying a good afternoon on the right wing.
But Elliott’s header, from a short throw-in routine, was the difference and the nature of the decisive goal annoyed Boothroyd.
“We did everything bar score in the second half and we played really during that period,” he said. “But the game is about fine margins; Cheltenham are a really good side and they put us under a lot of pressure just like we put teams under pressure.
“They scored a goal that came from our lapse in concentration - it was a quick throw, he lost his marker and scored at the second attempt.
“That’s something we have in our armoury, we don’t get done on it and we created lots of chances but just didn’t score.
“There are a lot of reasons for that and one of them is that Cheltenham’s defending was brilliant.”
Cheltenham move level on points with Northampton with the result but behind them on goal difference on another afternoon of league two twists and turns.
Boothroyd’s focus remains automatic promotion but he accepts the team will need to learn how to win matches like the one at Whaddon Road if they are to achieve that aim.
“If we want to be automatically promoted we’ve got to be able to win games like this one,” he said. “We’ve got to have fire in our bellies and be cool in our heads and we didn’t have that in this game, especially in the first half, we didn’t click.”