The Sulphurites lost a tight game which they controlled for long periods to Donovan Wilson's 30th-minute strike, slipping to a third consecutive League Two defeat in the process.
But, despite seeing plenty of the ball, it took until the dying moments of the contest for the visitors to create a clear goalscoring opportunity, substitute Jack Muldoon's close-range header from Ryan Fallowfield's inviting right-wing cross drawing a fine reaction save out of Dean Bouzanis.
“We didn’t create as many chances as we should have done when you take into consideration all of the territory and possession that we did have in the game," Weaver reflected.
“That’s where we were a bit short, in the final third. I thought we deserved something from the game, played some good stuff and largely in the ascendancy but the scoreline is all that matters.
"First two thirds of the pitch we looked good, final third, we didn't show enough quality on the deck. We didn't test their keeper enough.
"We tried to play on the deck. Some of the football second half was terrific - up to a point, because we didn't create enough."
Weaver has been openly critical of his side’s defending of late after a series of lapses and basic mistakes condemned them to defeat against Forest Green Rovers then Northampton Town, but on this occasion he said he could not fault his back-line for their efforts.
And although they failed to keep a clean-sheet for the 14th time in 15 matches in all competitions, the Town boss said he had to give due credit to Sutton’s Omar Bugiel for his eye-of-the-needle through ball and strike partner Wilson’s tidy one-on-one finish.
“The defence was so much tighter today, really determined, showed great resolve and a physical edge.
"I thought the centre-halves did really well, I think there was just one moment of quality first half from their two strikers, a great little through-ball through a tight space and a great finish.
"You can't always hammer the defence because we concede a goal. You've got to give credit to them for that execution and good finish and a good ball.
"We can take a lot of positives from the game. It would have been a really good away point against a team who are now third in the league, but it wasn’t to be."
Town remain 10th in the League Two standings after Saturday's defeat.