The Owls arrived off the back of impressive wins at Premier League Brighton and Leeds United, but were outclassed all over the pitch against a side who were winless in six.
Monk said he too shoulders responsibility for what was Wednesday’s worst home defeat for 19 years and apologised to supporters who filed out of Hillsborough in their thousands well before full-time.
“It was a horrible, horrible day for us,” Monk said.
“When you have a scoreline like that all you can do is apologise.
“There’s an emotion there and the anger and all the emotions that come with it will come our way and quite rightly. We deserve that.
“It’s difficult to analyse straight away but that’s two steps forward and a step back for us. Today was self-inflicted.
“The main part of it was the first 10 minutes of the game. We talk and train a lot around the first 10 minutes of games, especially at this level, where you try and take the foothold in the game.”
Monk admitted his side were ‘outclassed’ by a Rovers side that arrived on a run of six without a win.
The result sees them tumble from the play-off place and drop to 10th in the table, two points shy of sixth-placed Nottingham Forest.
While Monk said the dismissal of midfielder Massimo Luongo in the 26th minute was “100 per cent not a red card”, he refused to use the decision as an excuse.
“The problem was before that. We turned down the opportunity to play in their half, to get a foothold and get ourselves up the pitch,” he said.
“We kept turning out needlessly, playing our team mates into pressure and making needless mistakes. You can’t do that.
“We got the most heavily punished that we can do today.”