QPR draw with Sunderland
Aston Villa beat Reading 1-0 thanks to a late goal by striker Christian Benteke in another game between teams near the bottom of the table but the focus was on Redknapp's first match in charge at his fifth Premier League club.
“We worked hard and we deserved a point tonight,” Redknapp told Sky Sports.
“We defended well and denied them chances. I feel more optimistic tonight than on Saturday. I saw enough tonight to think we can go on a small run and keep ourselves in the pack.”
QPR, who have not won in 14 matches this season, remained rooted to the foot of the standings on five points, four adrift of Reading.
Villa climbed to 17th on 13 points following their third win of the season, level with Sunderland who are one place above them.
QPR came closest to scoring in the first half when Jamie Mackie was denied in a one-on-one situation with Sunderland goalkeeper Simon Mignolet and Adel Taarabt's follow-up shot was blocked.
Rob Green replaced the injured Julio Cesar in the Rangers goal at the start of the second half and made a brilliant save to keep out Steven Fletcher's powerful header.