Carl Heeley's side, which plays in the Conference North – the sixth tier of English football, saw off former FA Cup winners Coventry City at the weekend and now have the chance to create some more headlines.
Heeley said: "We will have to do the same as yesterday [Sunday] - it's all part of the magic of the competition and you just never know what will happen.
Warrington Town knocked out Exeter City in Friday's First Round Proper tie
"The tie will not hold any fear for us as we have already put out a League One side and we can do it again.
"It is another tough draw on the road, but we will give it a go as we've got every chance."
Perhaps the pick of the ties will take place in the north-east, as Blyth Spartans drew League Two basement side Hartlepool United, while Gateshead's game against Warrington guarantees at least one non-League side will feature in the Third Round.
Warrington manager Shaun Reid, brother of former England international Peter, said: “It's a good draw for us - they're a decent side and third in the Conference and we will have to do the same as we did in the First Round.
"We've just beaten a side with 100 places between us so we can't go into the game with any fear – that FA Cup trophy brings out the best in people so we will give it a right good go."
Warrington, of the Northern Premier League Division One North, are in the Second Round for the first time having caused one of the upsets of the First Round with their victory over Exeter on Friday evening.
And Reid joked of their next trip: "I am more worried about being in Newcastle the night before the match because that's a good night out and I know what my lads are like.
"I might have to look them up in their rooms or maybe go up on the day of the game!"
