Eric Kinder's side will be looking to start 2014 off on a high by progressing through to the quarter finals of the competition at St. James' Park.
Rovers defeated Hull City 3-1 to reach this stage, but come up against an Exeter City side that have already knocked out Torquay United, Crystal Palace and, last time out, Southampton.
"If you look who they have beaten, they've knocked Torquay United out in the first round which is a big game for them," said Kinder. "Then they've gone and knocked Crystal Palace out who are good at producing players.
"Then they have gone and beat Southampton which is a great result for them, a fantastic result. We know how strong Southampton are because we were only there a month ago.
"So fair credit to them, they've done really well to get that far and it will be a tricky game for us because we can't underestimate anybody and we certainly can't underestimate a side that has beaten Southampton in a cup competition.
"It'll be a long way to go, it will be a tough one for us, but if you'd have said to me either Manchester United away or Exeter City away I'd have gone for Exeter away, so it is up to us to be professional about it and progress again.
"It is a long way from home for us but this is why the Under-21 Premier League was developed, it is all about learning, we've got to travel overnight on coaches, you've got to play 300 miles away from home.
"If you want to get into first team football you've got a lot of time sat on a coach so we have to deal with that.
"We've done it at Southampton when most of these lads travelled a long way, so that's no excuse. We'll just get on with it, it is another game of football and a chance to progress in a competition that we want to go as far in.
ROVERS: Raya, Fernandez, R. Hanley, Paulo Jorge, Daly, Tumwa, Mahoney, O'Sullivan, Preston, Payne, Bauress, Edinho, Urwin, Pero, Lavelle, Pierce.