Redknapp took over from Mark Hughes in late November with QPR cast adrift at the bottom of the league after collecting just four points from their opening 12 matches.
While many believed the London club were destined to be sent straight back down to the Championship (second division), QPR have started to claw their way towards league safety and a 1-0 win at West Bromwich Albion on Tuesday put them in the next round of the Cup.
With Olympique Marseille striker Loic Remy and Rennes midfielder Yann M'Villa reportedly set to sign for the club, Redknapp believes QPR are on the right track.
"We're picking up some good results now and some clean sheets. We're getting the best out of the team at the minute," Redknapp told the club's website. "There are areas that I'd like to improve on, but I can't fault the effort of the players."
Redknapp was delighted with his side's 1-0 win in their FA Cup third round replay at West Brom on Tuesday, which came courtesy of Jay Bothroyd's late header and a string of vital stops from goalkeeper Rob Green.
"The first half was a bit dour. Rob Green made a fantastic save in the first half and then a number of others when he came under pressure after we scored.
"Jay Bothroyd did well tonight," Redknapp added. "He was at Sheffield Wednesday but he didn't do very well and they sent him back. I put him out there and asked him to show what he can do."
While the Cup win delivered a welcome shot of confidence, Redknapp emphasized the importance of securing their Premier League status for next season.
Redknapp, who saved Portsmouth from the drop in 2006 when they had looked doomed, has forged a reputation as a canny operator in the transfer market and the two expected arrivals from France could prove vital in the second half of the season.
He told British media France striker Remy, who had seemed set to sign for Newcastle United at one point, had passed a medical at Loftus Road while midfielder M'Villa was also poised to join.
Remy is expected to cost QPR 8 million pounds ($12.87 million) and M'Villa 7 million. Redknapp said Rennes had turned down a 28 million pounds offer for M'Villa last year, and Remy had once been touted at 20 million.
"The league is the most important thing. That is the key for us," he said. "You've got to try and stay up. The rewards for doing so are so big.
"But winning is a good habit. We've won twice away from home now after not doing so for over a year."
QPR, who are still bottom of the league but now just five points from safety, travel to 11th-placed West Ham United on Saturday.