Relegated Rangers started brightly and took the lead through Loic Remy's 11th-minute penalty, but Jose Bosingwa handed the Magpies a route back into the game when he pulled Hatem Ben Arfa's shirt to concede another spot-kick, which the Frenchman converted.
Bosingwa's mix-up with goalkeeper Rob Green then gifted Yoan Gouffran's Newcastle's second goal and the full-back failed to emerge for the second half.
"They were horrendous goals, both of them," said Redknapp.
"I thought it was a poor penalty and once we conceded the penalty we conceded another bad goal.
"It (crowd reaction to Bosingwa) was not going to help anyone. It was negative. He made a couple of errors but he didn't mean to do it and I took him off because we needed the crowd to be with us.
"People pay their money, we all get grief at some stages but it has been a miserable season."
Redknapp again insisted it is simply a lack of quality that has seen Rangers slip back into the Championship - where he thinks the current group would not even claim a top-half place.
"We are short of quality, it's nothing to do with character," he said.
"This team would not finish in the top half of the Championship. It's going to be very difficult to shift some of these players."