The former Hamilton boss has come under fire with the Carrow Road side suffering their fourth successive defeat and slumping to sixth in the Championship.
Norwich, relegated from the Premier League last season, were second in the table a month ago, but have now gone on a five-match winless streak.
Neil said defiantly: “The fans will be frustrated and annoyed and I understand that.
“My job is to win games. All I can say is that I am working extremely hard to turn things around and so are the players.
“I thought they worked extremely hard and kept going until the last minute. We did better in the second-half.
“You’re looking to stick to the task and not concede sloppy goals and then, as the game goes on, maybe quieten the crowd. But once we conceded that goal, it’s difficult.
“The two goals we lost in the first-half made it too easy for QPR.”
Neil’s task at Loftus Road wasn’t helped by the second-minute sending-off of left-back Martin Olsson for handling on the goal-line.
He was spared the loss of an early goal, though, when Tjaronn Chery dragged the resultant penalty-kick wide of the post.
Conor Washington gave the Londoners the lead midway through the first-half and Sebastian Polter added a second.
Scotland international Steven Naismith pulled a goal back to set up a tense finale, but it was too little too late.
New QPR manager Ian Holloway, who was in charge of the club between 2001 and 2006, returned following the dismissal of Jimmy Floyd Hasselbaink.
He said: “We got a lot of things wrong and I could see a lack of belief after Norwich scored. We stopped passing and using the extra man.
“But I was looking for character and I know we have it. Long may that continue.
“To win games at this level, you always need a bit of luck. All teams will have minutes of pressure, no matter how many players they have on the pitch.”