The Championship side won 8-7 on penalties after an entertaining third-round tie ended 2-2 after 90 minutes.
Jimmy Dunne thumped in the winning penalty after Tom Davies’ kick had been saved by goalkeeper Seny Dieng.
Benitez said: “It’s always bad to go out, no matter how, but especially when you play with a lot of intensity in a game like that. We have to be better if we want to go through and we didn’t do it.
“We have to learn from it and be ready to play against Norwich on Saturday, but tonight you have to be disappointed.”
Charlie Austin netted twice for QPR, opening the scoring and then restoring their lead after Lucas Digne’s equaliser.
Andros Townsend hauled the Premier League team level again early in the second half and they later appealed in vain for a penalty when Abdoulaye Doucoure went down under a challenge from Rob Dickie.
Benitez said: “It could have been a penalty but I didn’t see it (on video).
“But in this kind of game, when the attitude of the players is OK and you don’t win, you cannot be satisfied and it doesn’t matter what you say.”
Everton have been hampered by injury problems and will now need to assess Digne, who limped off with 10 minutes remaining.
Asked if Digne’s injury is cause for alarm, Benitez said: “Hopefully not. I don’t think it is very serious.
“We will see when we check tomorrow. We will have to assess it and then we will know more.”
QPR manager Mark Warburton savoured his team’s victory, particularly Luke Amos tucking away his penalty.
The former Tottenham midfielder was making his first-team return after nearly a year out with the second cruciate injury of his career.
At 6-6 in the shoot-out, Dieng saved Ben Godfrey’s kick but was deemed to have moved too soon, and the defender put away the retaken penalty.
But there was no doubt about Dieng’s subsequent save from Davies – or Dunne’s emphatic strike.
Warburton said: “It was a fantastic evening. Luke Amos stepping up and scoring in his first appearance after such a horrific injury – that’s what the cup’s all about.
“Luke is a great professional and has worked so hard to get back from two bad injuries. I saw him every day in the gym working his way back to fitness. His attitude has been tremendous.
“Luke deserved to get a great reception from the fans who know how hard he’s worked to get himself back fit.
“We were very good from the first whistle, were incisive and deserved the lead.
“In the second half we conceded early and rode our luck a bit, but then we got better as the half went on.
“The penalties from both sides were of such high quality and there was frustration for us when Seny saved it and it had to be retaken.
“The players to a man deserve so much credit tonight.”