The Gunners knocked the non-league side out of the tournament thanks to goals from Lucas Perez and Theo Walcott to set up a quarter-final tie with Lincoln City.
While Doswell was disappointed to see his club’s magical cup run ended he did reveal how the clash with Arsenal would alter their future and thanked the Gunners for their generosity.
"Arsenal have been superb and we think they will help us with a classroom," Doswell told reporters.
"They promised us £50,000 and that will buy us two classrooms, an amazing gesture and we are very thankful."
In the final minutes a plastic bottle was thrown at Arsene Wenger, though it did not hit him, and the game ended with fans running onto the pitch which Doswell criticised saying it prevented his fans from getting the reception they deserved for their exploits.
"It was a shame they couldn't get the round of applause they deserved," Doswell said. "It was a real shame people came on the pitch and took that away from them. I saw a few idiots shouting and screaming at Wenger and Arsenal players.
"You saw an idiot run on the pitch, that was the big moment of his life.”
"I'd have loved to have got a goal for the supporters. One of my little goals was to do better than Southampton and we have done that. They lost 5-0 to them and we lost 2-0 so in my mind that's a moral victory."
Sutton United will come back down to earth with a trip to Torquay United on Saturday afternoon.