Adel Taarabt produced a stunning display for QPR as he set up the opener for Jamie Mackie, won a penalty for Heidar Helguson to tuck in number two and wrapped up the scoring himself with a fine double.
There was little in the way of festive cheer on display, though, as a bad-tempered first half saw two straight red cards.
Clint Hill and Alan Tate were the recipients after the latter's foul on Kyle Walker sparked a sudden fracas.
Rodgers said: "I felt we started really well, created some chances and if we'd taken them it would have been a different game. Up until the sendings-off we looked comfortable. I thought 4-0 was harsh on us.
"But three of the goals we gave away were disappointing - although the final one was a wonderful piece of skill by a top player."
Source: PA
Source: PA