Tony Crane's first goal for Town on 71 minutes proved to be enough to put Town within points of the play-offs.
Groves made no denial that his team were fortunate, but pointed out that it's results and not possession that counts.
"I felt we were fortunate because we had to sustain a lot of pressure," Groves told the Grimsby Telegraph. "The lads had to dig in and we were under the cosh but that's what you get for a clean sheet and it's three on the spin for us now.
"I'm pleased with the defence and I'm also pleased for Tony Crane to score his first goal. He was a big man at the back and he put his body on the line for us.
"We have to be realistic and say we didn't play particular well and Blackpool were much the better side but this game is all about results and that's a good win for us."
With a huge game at the weekend against QPR, Groves will be hoping for a quick recovery on Mike Edwards who was taken ill and had to be replaced at the break by Greg Young.