"It was going to be a difficult game from the start, we knew that," said Boothroyd after his side's second-round exit at Blundell Park.
"Grimsby are doing well in the league and there are not a lot of spaces between us.
"We set out with a game-plan to frustrate them, to stop them and to break on them. We did that and I really couldn't see any real danger apart from a set-play, which we work on all week.
"But one man loses his marker and it's just a really, really poor goal to concede. The game then changes because you've got to chase it and then it's finished."