The Rs dominated for much of the game but conceded a late goal through a deflected Mladen Petric strike and Redknapp admitted the goal led to a tense final few moments at Loftus Road.
"We deserved it (the win)," he said. "I thought we were the better team and it would have been a travesty if we had conceded another goal in those hectic couple of minutes went they pushed (Brede) Hangeland up and bombed it into our box.
"When you have not won, psychologically the players must have been thinking 'oh my God' when they have got the goal and they think an equaliser is going to come, it must have been difficult.
"It was difficult for me watching that last four minutes and they must have felt the same but we hung in there and got the result we deserved."
The result moves QPR onto 10 points and above Reading into 19th place and Redknapp felt it was a necessity to end the winless run before they were cut adrift.
"At least it keeps us in there, if we hadn't won today it would have been absolutely desperate," he said.
"It is going to be tough, we are not going to kid ourselves but we have had one win but we are on a good run, we have had four games and taken six points.
"If you can take six points from every four games you will stay up - hopefully that can kick-start our season now and keep us going."