The top two, Macclesfield Town and Sutton United, were both defeated meaning Rovers could have climbed to within four points of top spot.
However, they were leapfrogged by Boreham Wood following their 2-1 defeat in Hertfordshire.
James Norwood had got Tranmere back on level terms before Bruno Andrade netted the winner for the home side ten minutes from time.
Mellon was angry with the manner of the winning goal and told the National League’s Oli Osborn “We never adapted well enough to the conditions and that was disappointing.
“We looked like the better side in the second half and were in the ascendency but got undone by a straight free-kick into our 18-yard box. We’re really disappointed with that.
“We’re fourth and my job is now to leave this disappointment behind and make sure the boys are ready for the next game.”
Rovers return to action next Saturday when they welcome Eastleigh to Prenton Park - a match that will be shown live on BT Sport.
“I’ll dust myself down and see if we can take anything forward from this game,” Mellon added.
“Then it’s all about getting the lads prepared for another important game at the weekend.”
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