A deflected Darron Gibson strike and Victor Anichebe's neat hooked finish five minutes either side of half-time kept the Toffees in the hunt for the top four but also ushered their visitors towards the Barclays Premier League exit door. Second-bottom QPR remain seven points from safety with only five matches left.
"I am disappointed. I thought the first half was going okay, there was nothing in it," a resigned-sounding Redknapp said. "There was a wicked deflection for the goal but I felt we came in 1-0 down feeling sorry for ourselves and then we started the second half sloppy."
He added: "Once we went 1-0 down we seemed to lose a bit of belief. We were indisciplined - kicking the ball away and getting two bookings. But you have to keep going. What else can you do? You can't give up and you have to keep believing but it is getting more and more difficult, obviously.
"It is hard but what can I say? I can't say we are down. If it happens, it happens."
While Redknapp contemplates the dreaded drop, Everton counterpart David Moyes has seen his side move to within three points of fourth-placed Chelsea, with Tuesday's opponents Arsenal just one point further ahead.
The victory keeps the Toffees' Champions League dreams alive for now, but Moyes knows their destiny is far from decided.
"I think if we can go and win at Arsenal then I think you might say we've got a chance of being involved in the Champions League," he said. "If we don't, I think you're probably going to say that we've got a chance of making the Europa League.
"So no matter what happens at Arsenal, the players have given themselves a great chance. We've been doing it for most of the season. Why would it change in the last five or six games?
"I expect the players to go and keep picking up victories and trying to win every game if we can."
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