"We can hold our heads up high," said Purdie, who was summarising the game on BBC H&W and Radio Five Live.
"But Fleetwood came down and did a really professional job on us. They were strong, fit and resolute - they knew what they were doing and were good for the win.
"If we'd had got a goal with twenty minutes to go, then all of sudden Fleetwood's confidence would've drained. If one of Dinsley's shots or Mills' free kick had gone in, then we would've had a great chance of getting something out of it.
"But it wasn't to be."
Purdie is currently sidelined with an injury, but he hopes to be back in contention for Sunday FA Trophy game.
"I ran quite a lot today, and if we'd had another training session before today then I probably could've snook on the bench, so I'm hoping to be involved on Sunday."
Ryan Green was disappointed that both of Fleetwood's goals were scored by Cian Bolger heading home a George Glendon corners.
"Disappointing, but we gave it our all. Everyone's given 100% out there, two set pieces but other than that they didn't really trouble us. They're a good team, four league above us.
"I'll have to see the goals again because I was behind the goalkeeper at the time marking a player, but I think Jack got blocked on the second one which the ref didn't see.
"Disappointed to lose on two set pieces, but that's football."
The Bulls were backed by a sell-out home crowd of over 4,000, and Green thanked them for their support.
"A big thank you to all the fans who have been our 12th man all the way through this FA Cup run.
"You can see how good they are as they cleared the pitch [of snow] in 12 hours which shows everyone's going in the same direction together."