Jamie Reed fired a last-minute equaliser for York to take the tie to extra-time, but Byron Harrison and Jack Midson struck for the home side before Reed grabbed a late second to make it a nervy final few minutes. Charlie Strutton had scored twice in normal time for the Dons after Seb Brown's early own goal.
York midfielder Scott Kerr was sent off for two yellow cards in the first half, but Mills said: "I thought from the word go we were excellent, we could have been 3-0 up. There's a big disappointment there, but we showed what we were capable of and if we keep playing like that we'll win football matches.
"I said to my players you sometimes don't get what you deserve in football and sometimes you do. We got what we deserved in the last game and it was the other one this time.
"From start to finish we were excellent and we worked hard to give ourselves an opportunity to go to penalties, but it wasn't to be and I'm gutted for them because they gave me and the club everything.
"I don't like to go on about referees, but we could have had two or three penalties - we didn't get them and I'm not saying that cost us, but we needed a bit of a break and deserved a bit of a break."