The Valiants looked like they were heading into the third round after Tom Pope’s second-half header but Jordan Green nodded home his first Yeovil goal in the 89th minute to force a match at Huish Park.
Every Town player on the field joined in with Green’s celebration, piling on the ex-Bournemouth winger and Way believes the equaliser was down to a lot of hard work and belief.
“The players are absolutely over the moon,” he told iFollow Glovers.
“They were a little bit anxious and nervy in the first half but that’s football. Some of them grew in confidence as the game went on and the fighting spirit they had, never giving up, certainly with the consequences of what potentially lies in wait, was very pleasing.
“To draw away from home and the fighting spirit the players showed, they deserve (the replay).
“I’m really pleased for them as they’re showing real commitment, they’re working really hard behind the scenes and the last-gasp goal was their just rewards.”
Way continued: “It does (feel like a win) because would you have thought we’d have pulled that back? Probably not.
“There’s one thing my group do; they keep believing, work extremely hard and when you work hard you end up getting more results and that’s what I see with this group.”
Town will know their potential FA Cup third round opponents on Monday evening.
In 2014, Way was part of the coaching staff that knew a win over Accrington Stanley in a replay would set up a tie with Manchester United and the Glovers boss hopes for another big occasion.
“I want the players to be excited when they watch the draw,” he said.
““In a 15 or 20-year career you only get these magical moments three or four times if that.
“We’ve been in this situation before where we could have had a disappointing result at Accrington but then we had the Manchester Untied tie so we’ll wait and see who we get!”