Rangers ended a three-game losing run with Wednesday’s shock victory at Stamford Bridge, but remain bottom of the table, five points from safety.
“After Sunday’s defeat by Liverpool it was difficult to convince anyone we could survive,” said Redknapp.
“But the players have set the standard with this win and to get out of this mess they have to do it every week.”
QPR had put up little resistance as they were well beaten by the Reds at Loftus Road, conceding three goals in the first 30 minutes.
But they responded by producing a battling defensive performance to frustrate in-form Chelsea before snatching the points through a late Shaun Wright-Phillips winner.
“That was our first away win in the league since October 2011 and let’s hope we can build on it. There’s still a long way to go but that was encouraging,” added Redknapp.
“The players worked their socks off and they got their rewards. We deserved it and it was a fantastic performance.
“We had a good meeting after the Liverpool match and I convinced the players we can stay up.
“Everybody else thought I was mad but I do genuinely believe it. We’re not doomed, we can turn it around.”
Things do not get any easier for QPR, who face Tottenham (home), West Ham (away) and Manchester City (home) in their next three League games.
But Redknapp hopes victory over their west London rivals, only his second win in eight games in charge of Rangers, will act as a springboard for their survival bid.
“If we keep working hard for the rest of the season we’ll win games away and at home,” he explained. “We have to make the most of that.
“The atmosphere in the changing room after the Chelsea win was fantastic, it’s the first time I’ve really experienced that here.
“I said to [coach] Joe Jordan after the game, ‘I cant remember having many better games than this one’. Chelsea were absolutely flying and we did it on the back of that Liverpool defeat.”
BBC Sport
