Bothroyd netted the only goal of the game as the Hoops beat West Bromwich Albion 1-0 in their third-round replay at The Hawthorns, while Green pulled off a number of fine saves.
Redknapp admitted that he was delighted for the duo, who have both endured frustrating seasons so far.
"Jay Bothroyd did well tonight," Redknapp told QPR's official website. "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.
"Rob Green made a fantastic save in the first half and then a number of others when he came under pressure after we scored.
"That's three clean sheets in a row, which is encouraging. We're picking up some good results now and some clean sheets. We're getting the best out of the team at the minute. There are areas that I'd like to improve on, but I can't fault the effort of the players."
The Hoops will host MK Dons in the next round of the competition, after they beat Wednesday in their third-round replay.