The Northern Premier First Division North side secured a 1-0 win at Cantilever Park on Friday night as defender Craig Robinson headed home in the first half.
Warrington Town 1-0 Exeter City
FA Cup First Round Proper
Friday 7 November
Cantilever Park, Warrington
Warrington receive £18,000 from FA Prize Fund
"Them boys deserve it," the ecstatic boss told the BBC after the final whistle. "Every one of them died for me, and we’ll go again.
"I said this morning that it wasn’t going to be easy, and they proved it.
"Fitness is just what’s in your chest, and sometimes you just have to go that extra mile, and they did."
With a spot in The Second Round now sealed, Reid says that he believes no-one will want to pull out an away tie against his men in the next round.
"On Monday, when it’s the draw, no-one wants to come here.
"I’ll have a think about that after a few glasses of wine. I’ll think about that on Monday – then we will go again."
And despite their Cup glory, the gaffer is refusing to let his players take their eye off the ball when it comes to their league campaign - and the club's fans.
"I’ve got to reach the play-offs. There’s a lot of good teams in our league, and it is very hard to get out of, but that’s our aim.
"I just hope they [the fans] are here on Tuesday when we have Stockport."
