The defeat once against saw Groves tactics brought into question as the long ball approach made little impact, with Iffy Onuora ineffective all game.
Speaking to the Grimsby Telegraph, Groves admitted that he blames himself for defeats and paid tribute to the travelling supporters.
"The first place you look after a performance like that is at yourself," he said. "I'm highly-critical of myself.
"I've asked myself if I could have done more to influence the game and I'm my own biggest critic.
"That's the way I am. I want to win so much and I want to do well and if there's any pressure right now, it comes from me.
"There was fantastic support. It's very disheartening for them to come in their droves and for us not to get a result.
"We were only on level terms in the first half and you have to thank them for coming, getting behind us in the way they did. We have to apologise for not getting a result."
Groves then went onto say that Phil Jevons could find himself dropped for the Bournemouth game, if Michael Boulding recovers. If Boulding returns he will return to partner Onuora, who Groves still sees as effective.
"I think in terms of the chances he (Jevons) had one or two. He got a goal from a free-kick and we're going to have to have a look at that and maybe one or two people will be looking over their shoulders.
"But as soon as we lost the physical presence up front we lost the impetus again until Craney went up there," he added. "Then we had a bit of it again at the death."