Exeter City manager Paul Tisdale insists there was "no shame" in his side's
The Grecians have only reached round two once in Tisdale's eight-year tenure at St James Park.
"There's no shame in it because I thought we played quite well, we just have to move on," he told BBC Devon.
"It's pretty disappointing, but well done to Warrington, they got their goal and they hung on."
The Northern Premier League Division One North side, who are 100 places below Exeter in English football's pyramid, got the decisive goal after seven minutes when Craig Robinson headed in at the near post from a corner.
"It's obviously something that wasn't particularly impressive about our performance. that corner, but other than that I think we played pretty well," Tisdale said.
"Other than not put it in the back of the net, we didn't do much wrong.
"We put a lot of pressure on them and they stood in front of the goal.
"We put the ball in the area enough for me to expect us to get a goal, by the way we played we deserved to get a goal, but we didn't and that's the way it is."
Exeter's sole first-round win under Tisdale came against non-league Nuneaton Town in 2009, but he was philosophical about their latest Cup setback.
"It's very easy to throw opinions at a team that's lost to a non-league club. A few years ago we lost at Curzon Ashton and we didn't do great and we didn't cover ourselves in glory.
"We didn't do badly (against Warrington), but we're out and that's the way it is," he added.