Despite creating the better chances - Leighton Baines hitting the crossbar with a free-kick and Tim Cahill missing a header from close range - it was the visitors who made the breakthrough in Saturday's Premier League contest.
Tommy Smith converted QPR's only real chance of the game in the 31st minute to secure the Londoners' first points on their return to the top flight.
Moyes had to leave experienced players Mikel Arteta, Marouane Fellaini and Louis Saha on the bench because of a lack of fitness, and with no money to sign anyone in the summer Everton came up short.
"The performance probably didn't deserve to lose over the course of the game but we did," said the Scot.
"We are the home team against a newly-promoted team and expected to make the play and score the goals, and we weren't able to do that.
"It wasn't because QPR dominated the game and outplayed us, we had good chances to make better opportunities and didn't do so.
"Tim missed a good one and we were a bit unlucky with Baines' free-kick.
"But if anyone is surprised and disappointed, they shouldn't be because we have been saying for a year or two we could do with an injection of wide players and centre-forwards.
"We are disappointed we didn't win because I thought we should have gone on and got a result."
The only bright spot for the Toffees was the performance of Ross Barkley, a 17-year-old academy graduate who made his first-team debut and was the best player in a blue shirt.
"I said to the players after the game I was disappointed with how they played but not to Ross," Moyes added.
"He got a big pat on the back. He nearly carried the team; he made chances, tried to take chances and looked really good.
"He's not long turned 17, we gave him a chance and he certainly didn't let us down."
QPR boss Neil Warnock was delighted to get their first points on the board after last weekend's 4-0 home defeat to Bolton, especially after a virus within the squad had restricted his options.
"In a way the attitude we came up with epitomised the whole result," he said.
"I said to them 'give me everything' and they fought for each other.
"I said 'let's go and enjoy it' because I'd rather be pulling up at Goodison Park than some of the Championship clubs we were last year.
"It was a well-worked move for the goal and they showed we can compete in the Premier League.
"In the circumstances we've had in the last 24 hours to do what they did was quite amazing and I couldn't be prouder.
"People like Patrick Agyemang (who started up front) were not in my thoughts for the last six weeks and at one o'clock, I had to tell him he was playing - it is like something out of a comic book."