It was a tale of two penalties at Blundell Park, with Jayden Stockley converting for the Grecians and JJ Hooper firing wide from 12 yards at the other end.
Both of those spot-kicks were awarded in a frantic 90 seconds before the break, while Exeter defender Kane Wilson later saw red for two bookable offences.
Wilkinson said: ‘Everyone wants a bit of luck, but we had our chances.
‘I thought we played really well, but the game changed with the two penalties.
‘The boys have been great. They competed really well, they worked hard and they gave me everything they had.
‘It was just that little bit of quality when we got the opportunity.
‘JJ scored one last week and was full of confidence. At the end of the day someone has to stand up and take it, but he’s obviously disappointed that he missed.
‘We have got to make sure, somewhere along the line, something goes for us.
‘We are going to have to battle, scrap and fight for the remaining 11 games. But I thought there were lots of positives to come from it.
‘We have got to build on it, and we have got something to build on, despite the result.’
Exeter manager Paul Tisdale added: ‘It was a very different performance to the game on Tuesday at Crewe but it was equally as important, with another three points.
‘It’s six points on the road this week and we feel pretty pleased with ourselves.
‘Grimsby deserved something today. If you were a neutral watching the flow of the game, you would say they deserved something, but we got our noses in front, just about kept it when they missed their penalty and we just dug in.
‘It’s the sort of performance where, again, Tuesday gave us confidence going forward, today gives you confidence, because we just defended so well and were so resilient and determined and made life very difficult for them.
‘They played really well today and Paul Wilkinson had them really geared up and they had some good play about them.’
Grimsby started the game on the front foot, but had to wait 20 minutes before their first chance arose, which Hooper blazed over the crossbar.
At the other end, home skipper Nathan Clarke bundled Ryan Harley to ground, with Stockley making no mistake with the resulting penalty.
Hooper then smashed his spot-kick wide for Grimsby, and there proved to be no way back after the break, either.
Jamille Matt came closest to a leveller, coming off the bench to plant a free header straight at stopper Christy Pym.
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