Goals from Lucas Perez and Theo Walcott – his 100th for the club – booked Arsenal a quarter-final place against another non-League team in Lincoln – but it was an uncomfortable night for Arsene Wenger.
Doswell said: “How do I feel? It can be summed up in five letters – proud. Very, very proud of my players. We asked them to give us everything that they had, and they did that.
“The two or three chances we had, you do need one of them to go in. I would have liked to have got a goal for our fans. But we did better than Southampton against them – they lost 5-0!
“It was a dream to watch my team play against Arsenal. The quality of the team they put out showed whats at stake. This was our cup final and these players will go down in history at the end of the day.
“Lincoln and Sutton have done our competition very proud. Best wishes to Danny and Nicky at Lincoln. Go and have your day in the sun like we have.
“It was a shame that our players couldn’t get the round of applause that they deserved at the end, a shame that people came on the pitch. It took that away from them – but they should be very proud.”
Wenger said: “We did the job. It is very different on this kind of pitch. It was not an easy game. We have to give them credit because every error we made they took advantage of. They played very well.
“It is basically division five and when I arrived in England 20 years ago in division five they were not as fit physically as they were today. Sutton were organised and had a huge desire. If we were not mentally prepared we would not have gone througn.
“I didn’t really enjoy tonight because we absolutely had to do the job and it is tricky. It is important for the confidence of the players.
“At Bayern we were 1-1 and then in the second half it all went wrong so at half time today at 1-0 up it was not finished.”
The only blot on the night for Sutton was when hundreds of fans invaded the Gander Green Lane pitch at the end of the game and confronted Arsenal supporters as scuffles broke out before police cleared the pitch.