Nedum Onuoha was credited with the opening goal after getting a touch to the ball following an error by former R’s keeper Rob Green, on his Leeds debut.
The visitors were better after the break but Tjaronn Chery’s 73rd-minute penalty and Sebastian Polter’s stoppage-time strike sealed a deserved win for QPR.
“It is obviously disappointing - not the start we wanted,” said Monk.
“We made a lot of mistakes individually and lacked that bit of intensity. You can’t give 45 minutes to the opposition like that.
“But this is just one game and I am confident we have the quality and the character in the group.
“It’s a process and I said when I walked in that it’s not going to happen overnight.
“There will be results that disappoint and also happy results. We want to make sure we get more happy results.
“I trust all my players and trust they’re good enough and will improve.
“I’m sure in the coming games and months we will see a lot of good results.”
Leeds’ travelling fans made their disgust clear, jeering their team’s below-par display and once again chanting for owner Massimo Cellino to step down.
Monk said: “We had great travelling support and had the intention of getting the right result and the right start to the season.
“We feel for them, feel frustrated for them, but it’s a process and there will be ups and downs.
“We will make sure we get a reaction. They will have a team to be proud of.”
QPR boss Jimmy Floyd Hasselbaink praised his team for making a fine start to the season but believes there is still plenty of room for improvement.
The Dutchman said: “It was a good start. Perfect? No.
“But it was a good start as we were organised and we had control in the first half and especially in the second.
“In the latter part of the first half I thought they had a better spell than us and brought us a little bit of trouble, although we didn’t give chances away.
“Half-time came at the right time for us but then in the second half we controlled it, had more energy and we played really well.
“We only gave away one chance really with our sloppiness and it was a good performance where we can have a look and work on things we need to improve and get better at.
“We need to try to get that consistency and that level of work. There are things to work on.”
Polter was a constant threat up front, but Rangers are keen to sign at least one centre-forward before the transfer window closes.
“We are still looking for that striker,” said Hasselbaink, who took over at Loftus Road in December.
“Hopefully we will bring some more in, because we need that help and need that competition.”