The Capital One Cup runners-up, beaten 5-0 in the final of that competition by Swansea in February, will be back at the national stadium on May 18 to face Northampton in a promotion shoot-out.
The West Yorkshire club overturned a 3-2 first-leg deficit against Burton on Sunday to reach the play-off final, winning 3-1 at the Pirelli Stadium to win the semi-final tie 5-4 on aggregate.
Parkinson was delighted to see the Bantams "win when it really mattered" but the insists his players have done that all season.
"This was a massive test and the players have come through it again," the Bradford boss said.
"We have had Wembley, Aston Villa twice, Arsenal and Wigan this season and after games of that magnitude it is very difficult to reproduce performances against the likes of Dagenham and Fleetwood away.
"It is almost a big-game mentality we have had. We would have liked to do better in some of our league matches but this season, more times than not, we have produced and been able to win when it really mattered.
"You have got to remember that some players and managers never get to Wembley. Supporters follow teams their entire lives and don't see them there, yet we are going back for a second time in one season.
"This group of lads have done it and you can't take away the enormity of that achievement. We said those big games in the (Capital One) cup this season would be important for the players in the future and once again we have produced when it mattered most against the team with the best home record in the division."