The Sulphurites debut campaign as a Football League club ended with a 4-1 loss on Saturday afternoon, a result which saw their hosts wrap up the title.
Town did in fact take an early lead through Jack Muldoon's 15th of the season, but failed to capitalise on a number of other good chances and were also far too open defensively.
And, although Weaver said that 2020/21 ending with such a comprehensive defeat shouldn't detract from what has been a very positive season for the club overall, he conceded his players must do better in both boxes.
"It's disappointing to go out with a whimper but we'd be being short-sighted it we just focused on today," the Harrogate chief reflected.
"It was a bit crazy that first half, we've created a fair amount of chances against the team that has won the title, but at both ends of the pitch, when we reflect properly, when you look at the stats - which don't lie - we've conceded too many goals this season.
"Today was another example of conceding far too many chances. The four that they scored today, there could have been more.
"Attacking-wise we were productive, to a point, but we need to be more ruthless and score more goals ourselves. We can still demand more.
"We have been in every game, and today was no different, we can be proud of that fact. We can take a lot from today because we have come up against such good opponents."
Weaver once again opted to give a number of the players who have been on the fringes of his squad this season a chance from the start against the Robins, though it took Town just seven minutes to break the deadlock.
Mitchell Roberts' left-wing cross was met by veteran Jon Stead - making his 700th career appearance. - and nodded across goal for Muldoon to head in.
Harrogate's lead was however short-lived, Liam Sercombe's 11th-minute shot slipping through the grasp of Joe Cracknell and over the goal-line before Sam Smith fired Cheltenham ahead.
The hosts went 3-1 up just after the half-hour-mark through Alfie May, then wrapped things up 10 minutes into the second period when Callum Wright capitalised on a poor clearance.
Defeat sees Town drop one place to 17th in the table, though they finish the campaign 12 points clear of the relegation zone, an outcome that Weaver is more than satisfied with.
"There's lots of ticks this season for this squad, lots of great moments that we can look back on, some great memories," he added.
"Yes, we've had some disappointments, but within those there have been important lessons that we've had to learn to grow again.
"The starting point is really establishing ourselves as a proper League Two team. We can't stand still, if we stand still for a moment, we'll slip backwards, and that's the fear that drives you on and also the excitement of thinking 'what is possible?'".