Captain Jamie Collins scored the winner from the penalty spot as the hosts stunned a team 83 places above them 1-0 on their artificial pitch.
Monk, clearly concentrating on promotion back to the Premier League - with a trip to Blackburn due on Wednesday night - paid the price for making 10 changes to his line-up.
“It’s a frustrating result and a frustrating performance but it’s my responsibility,” said Monk.
“I’m the one who selects the team. I made a lot of changes, it didn’t work and it backfired in that sense.
“All credit to Sutton. We wish them all the best in the next round. We didn’t want to see this happen, but it has.
“I stand by all the decisions I make. Sometimes you’ll suffer with decisions, but that’s life. I don’t regret any of them but when they backfire it is my responsibility.
“I don’t like losing any game. It doesn’t matter which one it is. I’m not a good loser and we’re trying to create a winning mentality - and when we lose we take it hard
Sutton boss Paul Doswell hailed a “huge achievement” by his part-timers – Collins’s second-half spot-kick ensured Sutton joined Lincoln in the fifth round, the first time two non-league teams have made it to the last 16.
“It’s a huge achievement by the players and the club to get to the last 16,” he said.
“I can’t praise the players enough. Every time they’ve been asked a question they have responded.
“Lincoln were an inspiration for us, and I can almost guarantee that will be the draw! We are due to meet them that weekend anyway.
“But at least then a non-league team will be in the quarter-finals. That would be a fantastic moment.”
Monk’s side, packed full of youngsters and including two debutants - neither of whom were even named in the squad line-up on the back of the programme - struggled badly on Sutton’s artificial pitch.
Roarie Deacon had a goal harshly disallowed after five minutes and the winger, whose five goals in the competition had fired Sutton this far, continued to torment the Championship side for the rest of the first half.
Sutton got the breakthrough they deserved six minutes into the second half, thanks to some shambolic Leeds defending.
Goalkeeper Marco Silvestri came out to meet Maxime Biamou but succeeded only in colliding with team-mate Lewie Coyle, taking the Sutton forward out and giving referee Stuart Attwell little option but to point to the spot.
Collins, a builder by trade, stepped up and nervelessly sent Silvestri the wrong way to spark wild celebrations on the old-style terraces behind the goal.
As if Leeds’s afternoon could not get any worse, they were reduced to 10 men with 10 minutes left after captain Liam Cooper was sent off for a foul on Craig Eastmond.