The Sulphurites once again failed to score from open play as they were edged out 1-0 at Wetherby Road, Kian Spence’s fine 21st-minute strike from long range enough to settle the contest.
Jack Muldoon spurned a glorious chance to equalise when he missed a second-half penalty, but otherwise visiting goalkeeper Paul Farman was barely troubled.
"I thought that we were asking questions without looking deadly, I think that is a fair assessment,” Weaver reflected.
"It didn’t feel like a goal was definitely coming. It was working to a point, but the final ball was missing.
"We might not have had the quality to unlock their defence or create an opportunity to score, but the least people want to see is passages where we at least tried to play - albeit we weren’t good enough.
"Barrow have got a super-physical, powerful squad now that has evolved in the summer. They’re direct, hard to handle and we succumbed to that, we couldn’t get going.
"We have to challenge ourselves to play like we train and get on the ball and pass it because we don’t practice booming it 60 yards. We have got to challenge the psychology, challenge the bravery and demand more because, as I said to the lads after the game, there’s no point in us just launching it because people won’t turn up to watch that.”
Town’s only real opportunity to get themselves back in the contest came in the 61st minute when Anthony O’Connor’s header from a corner was handled by Rory Feely.
Muldoon was however unable to take advantage, firing a woeful effort from 12 yards straight at Farman.
"Jack apologised to me straight after the game,” Weaver continued.
“But he didn’t need to apologise to me, he is one the best players in our history in terms of big moments.
"It happens to Mo Salah sometimes, it happens to the best in the world, so it can happen to Jack.
"It was unfortunate because that could have triggered a really positive performance and result, but it wasn’t to be, so I’m not going to kick him while he is down.”
Saturday’s result leaves Town 19th in the table after six matches with just six points to their name.