The Glovers boss had 10 outfield players to choose from on Wednesday before securing four loan moves at the end of the week.
One of those new recruits was Southampton youngster Marcus Barnes who netted the opener against the Bantams, before Jordan Green sealed victory late on.
“We were the underdogs but the result tastes even more sweet because of the week we’ve had,” Way told iFollow Glovers.
“The players have been very focused despite the uncertainty. On Wednesday I think we only had 10 training and then for Surridge to go down… everything was against us.
“It’s an absolutely extraordinary achievement from my players. The football club deserves it.
“We were up against a really good Bradford side who are in the play-offs with 30 to 40 players to choose from and we looked very dangerous against them.
“We made sure the players who crossed the white line believed they were the best and that’s what I felt.
“We said it was an opportunity for the players to create a little bit of history and with that result everyone will remember them for that. We now look forward to Monday’s draw.”