Laurence Maguire headed the Spireites in front on six minutes from Liam Mandeville’s cross.
But the Mariners turned the game on its head midway the first-half with two superb long-range strikes from John McAtee and Gavan Holohan.
Harry Clifton headed in a third five minutes after the break and Ryan Taylor swept in a fourth late on.
Cook, who said his side ‘did not work hard enough’, said: “We were absolutely miles off it in terms of the performance.
"I can’t say we capitulated because that is a ridiculous statement but we gave up the game very easily.
"To lack contact all over the pitch and aggression and not winning individual battles was alarming. That is probably the first time I have seen that in the Chesterfield team since I have been here.
"Grimsby have played ever so well today, they have had a really strong performance and they have left us licking our wounds and we have got to be better.
"Us managers are supposed to come in and give you all the answers but sometimes you just don’t know do you. One thing I do know is that if you give people time and space on a football pitch they will hurt you and we got hurt today due to giving time and space.
"We want to have contact and engage all over the pitch and be competitive but that was certainly not the case for us today.”
The defeat for Chesterfield means they drop to fifth in the table.
Cook added: "For us it is a really disappointing day. We have to go away, train harder and want to get better.
"At the minute we are probably not scoring enough goals that we all crave. We have missed a couple of big chances today and we have also hit the post.
"But I am not one for making excuses, we were second best today.
"We got what we deserved, not probably in terms of the scoreline but certainly the result.
"Today, in my opinion, we did not work hard enough to get where we want to be.
"We started well, scored a goal, but we didn’t earn the right to do anything after that.