The disgruntled travelling support treated Rodgers to a chorus of 'you're getting sacked in the morning' and chanted former boss Steve Coppell's name as the goals rained in against the woeful Royals.
Reading are now just three points off the foot of the Championship after they were blown away by strikes from Akos Buzsaky, Jay Simpson, Rowan Vine and Patrick Agyemang.
"It was a tough night," admitted Rodgers.
"I can understand the reaction. I've never experienced that but I've always been taught to fight. I'm not worried. Better managers than me have had that.
"It's not nice but can you blame them? We were poor. But it just makes me more determined.
"We've had a horrendous start. But what people maybe don't understand is it's a massive task here. My ambition at the beginning of the season was to be up there, but the reality is it's a very difficult job - all the best players have left.
"I want to give people a chance but I can't watch too much of that."
Rodgers may have thought his luck was about to turn after half an hour when Ben Watson was shown a second yellow card by referee Andy Hall for taking a free-kick too quickly.
"It was a poor sending-off," said Rangers boss Jim Magilton.
"It's the letter of the law but common sense must prevail. We are all grown men."
But Hall had actually done Rangers a favour as Buzsaky stepped up to take the same free-kick and curled it into the top corner.
The 10 men doubled their lead eight minutes later when Wayne Routledge floated in a deep cross which fooled Adam Federici and Simpson volleyed in at the far post.
Hall evened up the numbers less than 30 seconds into the second half, although he had little choice after Ivar Ingimarsson, also on a booking, scythed down Simpson.
Substitutes Vine and Agyemang grabbed their first goals of the season to put the gloss on another fine performance - Rangers have now scored 13 goals in their last three games whereas Brian
Howard's late consolation was only Reading's 11th of the season.
And former Ipswich boss Magilton sympathised with his opposite number.
"It's horrendous. I've been there, and I was ninth in the table at the time," he said.
"So I have a great deal of sympathy for him because you have to take the brunt of it, and you have to carry the can and he'll be up all night thinking about it."