The Glovers dispatched Port Vale in the second round and are now looking to improve on their record that has seen just two defeats in their last seven matches.
Otis Khan (twice) and Francois Zoko were both on target in the extra-time win over the Valiants, while Matt Worthington was named man of the match having come off the bench.
Way was impressed by his side’s endeavours on Tuesday night and now has things to think about ahead of Saturday’s trip to Mansfield Town (3pm).
He told iFollow Glovers: “Every player that played on Tuesday, with the level of commitment and effort they put in, will be looking for a starting place.
“Any away game can always be difficult just because the majority of the players – certainly the 14 or 15 new players I’ve got – have never experienced playing in a new ground.
“There’s different noise, different pitch dimensions, even though that shouldn’t make a difference.
“I feel one or two of the younger players have not stood up to mark and we have to make sure as a team we put in a really good performance and that will take 11 individuals at the top of their game to get those three points.
“Having said that, with the experience they’re gaining – when you look at Port Vale away and the way we came back into that game – it shows that we’re making improvements.”
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