Rangers had a number of players missing at Blundell Park and Holloway felt that the changes he was forced to make caused him real problems against a lively Mariners side.
"I thought Grimsby thoroughly deserved the result. I thought we might ride it out, but the first half just wasn't good enough.
"We were overstretched with injuries and it showed this afternoon.
"The effort and the spirit in the second half was excellent, but I have no complaints, we lost to the better team on the day.
"No matter what we tried to do, it didn't really work. The goal itself came out of nothing but sometimes you have to take it on the chin and accept that you got what you deserved.
"We knew the tie would be difficult but we had to call two young lads back off loan and that didn't help."
Martin Rowlands limped off in the second half to add more worries, although Ollie was unsure about the extent of the injury.
"I'm not sure how serious the injury is - he felt his groin and came off as a precaution."
Yet despite this afternoon's defeat, Ollie ws phlegmatic and admitted that his focus was already elsewhere.
"The league is the priority to be honest. We were never going to win the FA Cup - the focus is on winning promotion.
"Just look at the injury problems that the LDV game caused us. Now we turn to Tuesday's game against Brentford."