Holbeach United recorded a fifth successive win - but manager Seb Hayes was unhappy with “the worst performance so far this season”.
A stoppage-time goal by substitute Jordan Keeble sent the Tigers into the first round proper.
Lewis Leckie’s opener was cancelled out by Huntingdon Town and Rick Drury saved a second-half penalty.
Hayes said: “It was a bad day, despite the result.
“Our captain Nick Jackson couldn’t play because his partner went into labour, Joe Braithwaite should have been left out as he had a vertigo attack before the game and Mitch Griffiths went off early with a hamstring injury.
“I’ve got to learn as well as I made bad decisions and luckily they didn’t cost us.
I’ve got to learn as well as I made bad decisions and luckily they didn’t cost us.Seb Hayes
“Matt Warfield and Joe Smith were suspended so we were struggling.
“When we got ourselves 1-0 up, I thought we would push on and punish Huntingdon.
“But they got back into the game from a free-kick with some woeful defending where we didn’t pick up runners and they slotted in unmarked.
“We changed our shape in the second half and Keeble’s introduction made a massive difference out wide.
“Drury made a brilliant save from the penalty and that also ignited our play.
“We had so many corners plus a disallowed goal and one off the line.
“Overall, though, we didn’t play well at all.
“Huntingdon didn’t cause us problems as we dealt with them during the second half when they looked to play on the counter-attack.
“We weren’t at the races. We are making three or four changes every game due to injuries, unavailability and suspensions.
“Sooner or later, we will get caught out and it could have happened on Saturday.
“We didn’t deserve to lose. But we didn’t deserve to win it either. As the lads said after the game, we were rubbish and we won.
“The positive is we scored another late goal. Keeble’s header was going in before it hit a defender so I don’t think it’s an own goal.”