The point earned the hosts a top-10 finish in their maiden east division season.
It was a ninth game in 21 days for Moneys, who fell behind after missing a penalty at the start of the second half.
Lewis Fennemore popped up with an equaliser.
Dave Carter is satisfied with the way his side have coped at the higher level.
‘We started the season with a 15-game unbeaten run and ended it unbeaten in seven,’ said the Moneys boss.
‘It was just the bit in between that was a problem.
‘Our target was a top-10 finish and we achieved that.
‘It was a proper end-of-season game against Cambridge.
‘We had chances to win it.
‘Joe Briggs missed a penalty and a couple of other opportunities wouldn’t quite go in.
‘Their goal was a bit contentious because Tyler Giddings cleared but the officials ruled the ball had crossed the goalline.’
Moneys must now wait to see where they will be playing next season.
Restructuring could see them end up in the Ryman League or the newly-formed Southern League west division.
Meanwhile, Paulsgrove were crowned Hampshire Premier League champions after a 6-2 win at Colden Common.
Danny Lane fired a hat-trick with Jimmy Hird, Josh Parry and Craig Ralph the other marksmen.
Lane, who has 30 goals this term, will have further opportunities to increase his tally when Paulsgrove travel to Infinity tonight and Winchester Castle on Wednesday.
On Friday they meet Liphook in the Hampshire Intermediate Cup final at Wicor Rec (7.45pm).
Jake Alford put Fleetlands ahead against QK Southampton but the visitors hit back to win 2-1 at Lederle Lane.
Joseph McIntosh and Harry Potter hit the target as Clanfield beat Winchester Castle 2-1 at Peel Park.