The 1-1 draw prevented Rod Stringer's team moving clear at the top of the Vanarama National League South.
Weston had endured put a poor start to the season behind them by thrashing Wealdstone 5-1 last Tuesday.
The point at Melbourne, sealed by their debutant striker Irnti Rapai eight minutes from time, should have pleased boss Marc McGregor.
But he was actually wondering what might have been after returning to Somerset from Essex on Saturday night.
"It’s a tough place to come, but on the day we deserved to come away and win," the manager told the Weston Mercury.
“With a bit of luck we could have scored three or four more than we did.”
The Seagulls are on the road against on Tuesday night and they face an Oxford City side who have been letting in too many goals.
Then on Saturday it's FA Cup duty and Weston face divisional rivals Oxford City.