The Glovers were reduced to nine-men on the stroke of half-time and battled hard to keep the Red Devils at bay before a lengthy stoppage due to a drone assisted the visitors’ winner.
Sky Bet League One side Bradford City head to Huish Park on Saturday (3pm) looking to reach the fourth round for the first time since their quarter-finals exploits in 2014/15.
Way is aware of the threats the Bantams pose and calls for his players to produce another big defensive effort in order to progress.
“We only had nine players but we defended really well with the players that we had,” Way told iFollow Glovers.
“The way they defended was magnificent. What we’ve got to do is do that against a good Bradford team.
“They’ve scored good goals. We’ve come up against (Charlie) Wyke a number of times; he’s very, very dominant in the box, but we’ve talked about his threats with the defenders we’ve got and they’ll be ready for the challenge.
“We know the consequences (of winning) and Yeovil seem to have a really good history of creating stories; Saturday is our opportunity to create a really good story.”