The Sulphurites were aiming to end their second season as a Football League club with a flourish and make it three wins on the spin, but lost what was an action-packed encounter to goals in each half by Craig Eastmond and Isaac Olaofe.
And, while the U's certainly could have scored more than twice themselves, the home side had plenty of clear-cut chances of their own, twice hitting the woodwork at 1-0 when they seemed destined to equalise and drawing a number of good saves out of Dean Bouzanis.
"We missed some gilt-edged opportunities, didn't we," Weaver reflected.
"We did enough to score goals today, but probably didn't do enough to keep the back door shut. So, inevitably, when you don't take your chances, you leave yourself open to losing an end-to-end contest like this.
"We caused them problems when we passed the ball. That was the game-plan, we have just got to get better at it.
"I'm disappointed overall because I really wanted to finish the season with three wins on the bounce after two extremely positive results against Carlisle and Forest Green.
"When all is said and done, no matter what plaudits we get for playing well in an exciting match and creating lots of chances and hitting the woodwork, at the end of the day we've lost the game and it still hurts you because we're winners are Paul Thirlwell and I."
Rory McArdle's 16th-minute header from George Thomson's right-wing corner rebounded off the inside of the post shortly after Eastmond had nodded Sutton into an early lead, while Alex Pattison and Jack Muldoon both brought the best out of Bouzanis and Luke Armstrong fired narrowly over as Town pushed for a way back into Saturday's contest.
But, their clearest opportunity fell to Diamond on 66 minutes, when he was played clean through and confidently danced around Sutton's number one, only to roll his finish against the base of the upright with the goal gaping.
"Jack Diamond scores his chance 99 times out of a 100, he doesn't make a habit of missing those opportunities," Weaver added.
"It was a great run by him and a fantastic pass through by Warren Burrell, and that's the kind of thing we want to see more of, but obviously the finishing touch just wasn't quite there.
"In the big moments, we weren't quite good enough in terms of putting the ball in the back of the net."
Saturday's defeat sees Town drop two places and finish the season 19th in League Two with 53 points to their name from 46 games.