James Berrett levelled at the death after David Worrall had opened the scoring in the 10th minute at Blundell Park.
Home goalkeeper James McKeown also saved a penalty from Michael Tonge, as the relegation rivals were ultimately made to settle for a point each.
Jolley said: ‘There are a million things we can look to improve on, but the lads showed they are willing to go until the 90th minute to get something from a game.
‘I was really pleased with the psychology of my team.
‘We were proactive with our changes and we tried to affect the game.
‘We have taken a point from the game and there is something to build on. It was a good start and we can now look to improve.
‘We have had a positive week and they have done well. There are a few things we need to work on, but we are one point closer to what we need.
‘I also thought the fans were fantastic, and we will need them right up until the end of the season.
‘It’s going to be a bumpy ride, and we’re not going to win all 10 games, but it was a good start.’
Third-bottom Vale, without top-scorer Tom Pope, are six points clear of the relegation zone.
Manager Neil Aspin added: ‘You would have to say we deserved to win the game, but for a world-class display from the Grimsby goalkeeper.
‘You are disappointed that you haven’t won the game, but I’m pleased with the efforts of the players and that is the most important thing.
‘They showed enough fight and determination to show they can stay in the league.
‘We are unfortunate that Tom Pope is the penalty taker and he wasn’t playing. Tongey (Michael Tonge) said he would take them and it’s a good save from the goalkeeper.
‘You expect to score a penalty, but it’s not that easy.
‘He had the guts to take it and it was a crucial stage of the game, but these things happen in football.
‘We looked a threat today and we made chances. We didn’t sit back. You are always going to miss someone like him, but we coped well.’
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