A 79th minute goal from Wigan striker Will Grigg settled the tie and ended City's hopes of a clean sweep of all the domestic trophies.
And City's England central defender said the result was a bitter blow with the Blues having dominated possession and territory at the DW Stadium.
"They got one chance and scored it. It's our own fault we're out of the FA Cup," Stones reflected.
"(The feeling in the dressing room) is massive disappointment for ourselves.
"We want to be competing in all four competitions until the end. Tonight was a final for us but it's never easy, coming away to a lower league team with the conditions and everything that comes with it.
"It's a blow. I can't say much more."
City's cause was hampered by the crucial 45th-minute sending-off of defender Fabian Delph.
Referee Anthony Taylor showed the England international a straight red card for his challenge on Max Power, forcing Pep Guardiola's side to play the second-half with just 10 men.
But Stones refused to use Delph's dismissal as an excuse for the result.
"It was a difficult one. Obviously the sending off was a big factor in the game but I thought we deserved to get a replay at least," Stones added.
"They had one chance and scored.
"The sending-off had a big effect. You need 11 players on the pitch at all times. I can't say whether it was a red card or not as I haven't seen it.
"It's one of those things and you have got to deal with it and carry on. I thought we dominated the game and created a lot of chances and we should have won it."