The Welsh club suffered a 5-0 thumping at home to Chelsea in the Premier League last weekend and were looking to return to winning ways against Championship opposition at Ewood Park.
Rudy Gestede and Craig Conway scored late on to seal the the upset, after Chris Taylor had cancelled out Gylfi Sigurdsson's stunning opener.
The visitors had seen Kyle Bartley dismissed following a coming together with Josh King early on, before a late challenge on Taylor during second-half stoppage time earned Sigurdsson a red card of his own.
And Monk conceded his disappointment at failing to pick up what would have been a morale-boosting win.
"It's a disappointing result to go out of the Cup," said Monk. "We wanted to get back on track, but unfortunately we couldn't do that.
"To go down to 10 men early on didn't help. All the preparation you do before the game kind of goes out of the window.
"We tried to restructure to get to half-time to regroup and we scored a good goal, but they got the equaliser before half-time.
"We talked about how we were going to work in the second half to keep in the game until towards the end, then maybe change formation to have a go. We were doing that, they didn't have too many dangerous situations.
"But we conceded a poor second goal. It was poor marking at a set-piece, which is something you can't afford to do at any level. The third then comes because we were pushing on.
"We're in a difficult moment after the last two games, but it's important we come through it together."
On the two red cards, Monk added: "The first [Bartley's] was a coming together, but you run the risk of that when you are the last defender.
""I thought the second red card [Sigurdsson's] was harsh. It warranted a yellow, but I don’t think it was a red.
"He had a lunge after he was kicked. He shouldn't react, but it wasn’t dangerous.
"I don't think he was in any danger of hurting the player."
