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Palace chairperson Steve Parish ended Warnock's five-month reign on Saturday after the south London club slumped into the Premier League relegation zone, but caretaker manager Keith Millen convinced his players to ignore the turmoil and they delivered an improved performance at Loftus Road.
The Eagles, linked with moves for former Tottenham boss Tim Sherwood and ex-Porto chief Vitor Pereira, remain in the bottom three on goal difference, while QPR are two points above the drop zone.
Millen, in his third spell as caretaker, made one change to the Palace team beaten by Southampton on Boxing Day, with Wilfried Zaha replacing Fraizer Campbell up front as the Eagles looked to register a first win in seven matches.
Both teams looked short of confidence and composure in a scrappy opening and QPR striker Charlie Austin should have done better than shoot straight at Palace goalkeeper Julian Speroni.
Yannick Bolasie produced Palace's first real moment of quality when he unleashed a powerful strike which Robert Green was at full stretch to keep out.
The visitors went even closer in the 21st minute when Joe Ledley picked out Jason Puncheon and the Palace winger curled in a first-time effort that beat Green but rebounded to safety off the post.
After failing to build any momentum in a drab first half, QPR went close to breaking the deadlock soon after the interval when Leroy Fer's volley flew just wide.
Fer forced Speroni to show his athleticism to get a hand to a powerful strike from the Dutch midfielder as QPR finally found some rhythm.
Austin had a goalbound header blocked from a corner soon after and Puncheon's shot was tipped over by Green at the other end.
Millen responded to his side's struggles by sending on Campbell for Zaha midway through the half.
But Harry Redknapp's side went agonisingly close to taking the lead in the 75th minute when Steven Caulker nodded goalwards from Joey Barton's corner, only for James McArthur to alertly head clear from under the crossbar.
And QPR spurned one last chance when Junior Hoilett failed to hit the target with a clear sight of goal.
