Jay Matete gave the Mariners the perfect start with a goal inside a minute and Bolton struggled throughout to cope with the physical threat of James Hanson and Lennell John-Lewis.
Both sides missed a hatful of opportunities with Bolton’s best falling to Eoin Doyle, Kieran Lee and George Thomason.
Sub Ira Jackson Jnr put the result beyond doubt with a goal four minutes before the end, with Shun Miller grabbing a consolation for the Whites deep into stoppage time.
Evatt had warned prior to the game that Grimsby would be dangerous opponents as they scrap for points to preserve their EFL status.
And so it proved as Bolton failed to live up to the high standards they have set in recent weeks.
“I knew what was coming,” Evatt said. “There were just too many under par. Too many not playing their level and when that happens in a difficult game against a team fighting for their lives in difficult conditions, you end up losing games.
“Add to that the chances we’re creating and missing, we certainly don’t help ourselves.
“But we’re still in a great position. I’ve just said to them there we’re still in a fantastic position and we can’t forget that and hopefully that will kick us on for the next four games.
“We’ve got a home game to come on Tuesday and we willl park that now and get ready for then.”
Wanderers went into the game knowing they could go top if they bettered Cambridge United’s result at Newport.
They had been given a pre-game boost as Cheltenham were beaten 1-0 at Crawley on Friday night.
But their failure to take advantage was a disappointment for Evatt, who admits his team lacked the clinical touch they needed.
“There isn’t any margin for error and we’ve been saying that all along,” he said. “You just can’t predict results in this division.
“I said in the week that these were eight unbeaten before Saturday when they lost with 10 men so they’re not playing badly and they’ve had results against the top teams as well.
“I think other than the first 40 seconds and the few set pieces in the first half, we took control and then we created lots and lots of chances.
“We just, for whatever reason, aren’t taking them at the moment and then second half we started slow again.
“Credit to them, they put us on the back foot and Gillo made some fantastic saves that really he had no right to save and we had a chance and then again we’ve missed I don’t know how many opportunities.”
Evatt insists missed opportunities are not a reason for serious concern.
“For a number of reasons,” he said. “One, at least we’re creating them. I’d be more worried if we weren’t creating chances and two, we have goalscorers that predominantly take those opportunities and sometimes for whatever reason, you can have little dips in form, little dips in concentration in our final decision.
“But I said to the players, we can’t keep relying on Eoin (Doyle) to score the goals. Everybody had to step up to the plate and other people have had fantastic chances of late and not taken them.
“We have to start taking them, it’s as simple as that because a lot of our work has been really good. But it’s not just the shot, it’s the final cross, how many times do we get into the final third and all we’re looking to do is pick somebody out and we hit the first man or pick out one of their defenders? We need to be better.”