In a match dominated by defences, clear-cut opportunities were at a premium although both sides had chances to snatch a win.
United, missing influential midfielder Kevin McDonald due to injury, found themselves under the cosh during the early exchanges but still forced the two first chances of note with Nick Blackman blazing over following an exchange of passes with Ryan Flynn and Tony McMahon forcing an excellent save from Owain Fon Williams.
Jake Cassidy and Andy Robinson went close for Rovers after the break while Blackman shot wide from an acute angle.
Wilson said: "We knew how hard Tranmere were going to be. You've only got to look at the table to see that.
"They are where they are on merit and we are too.
"In a sense, it was a bit frustrating because we went into that match wanting all three points.
"Defensively, though, I thought we were superb and so that was very pleasing.
"We just needed a little bit more magic up front, perhaps a little bit more patience at times. But we've got some young lads up there and so that's to be expected."