Dutton, who had seen his side hold the bottom-of-the-table Mariners to a one-all draw at Blundell Park, admitted he was hoping for a win but believes Walsall are that little bit closer to securing safety.
The Saddlers had arrived at the clash on the back of a goalless draw with second-bottom side Southend United, but were unable to secure three crucial points, which would have seen them earn just their second victory in eighteen games.
Dutton's team fell behind with just nine minutes on the clock as James Hanson netted for the hosts but were able to get themselves back on level terms just before half-time as Caolan Lavery scored his seventh of the season.
Sadly, the Reds were unable to add to their goal as another second-half slump saw them offer very little in the final third, ultimately taking just one point from a contest which many considered to be a six-pointer.
Speaking to the assembled media, Brian said; "It wasn’t the win I was after but to be honest, if you told me I could take a point each from Southend and Grimsby, I would have probably taken it.
"Simply because that keeps the wolves from the door and leaves us with fixtures that we can go and attack now.
"Grimsby and Southend have to do something pretty phenomenal between now and the end of the season to overtake us.
"That was the main objective, to keep the wolves from the door, and that’s what we’ve done.
"I’m delighted to come away from here with the point and an improved performance. We need these lads to step up to the mark and make impacts, and that was the war cry, and they did that in abundance.
"It was a big gut-check for the boys, and they haven’t let me down on the gut-checks. They’ve let me down with quality in certain games, but in terms of the gut-checks, we’ve only ever lost games by the odd goal.
"They needed to react, and I thought they did."
A win for Southend over Harrogate Town means the Saddlers will head into their Good Friday clash with the Sulphurites with just a six-point advantage over the drop zone.
However, with the Saddlers having a game in hand over their relegation rivals Dutton believes his team will avoid the drop, with the former development coach insisting other teams are under pressure too.
Dutton added; "It leaves Grimsby and Southend in the same situation doesn’t it. They’re six points behind with us having a game in hand.
"It’s a tough ask for them but all we can do is concentrate on ourselves."