The Saints face an exhausting trip to Cumbria on Tuesday night for the second round replay.
The draw threw up a big reward - and whoever wins the second match at Holker Street will face a home tie with Sutton United of the National League.
Wilkin was delighted by the display from his side, and although the game ended 0-0 he said it proves that his team can mix it with strong full-time sides.
“We marshalled them very well and I can’t really remember too many chance that they’ve had,” he said.
“Scoring goals is the hardest thing to do in football and neither of us have so we go again on Tuesday.
“We’ve had some good moments, and it was a strong performance - we want to challenge ourselves and see where we’re at. They’re not a bad side Barrow, so it gives us a good indication of where we are.”
With extra time and penalties possible, Wilkin knows Town will be getting home as the milkman starts his shift on Wednesday morning.
But he wants a shot at doing something special - and with many National League clubs already exiting the competition, the chances are growing by the game.
“A replay is not ideal, our league campaign is a priority for us but we will have to go up there and give it our best shot,” the manager said.
“We need to get a few bumps and bruises sorted out and if we can I’m sure we’ll give a good account of ourselves.
“We’ve been strong in the league and have had some good performances but the results lately maybe haven’t mirrored that. If we can stay strong and focused then we give ourselves a chance.”