Adkins said: "The players were fantastic yet again. We did great in the first leg to get a 2-0 lead and we came out this time and put in a very professional performance.
"We can look forward to a trip to Wembley now the game is all about supporters and we've tried desperately hard this season to put a smile on people's faces and try to play the game the right way.
"We set our stall out to win this tournament and we're one game away from that now and the supporters can look forward to a great day at Wembley."
Scunthorpe will play Luton at Wembley on Sunday April 5. As a consequence, the League One fixture at Northampton scheduled for the Saturday will have to be rearranged.