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 the former England keeper made a brilliant save to keep out Steven Fletcher's powerful downward header from a corner.
"I was hoping we would win the game," Sunderland manager Martin O'Neill said.
"I know QPR will be buoyed by Harry Redknapp's appointment but I thought we could create enough to win. There were chances at both ends but it was a frustrating evening."
Redknapp, 65, who chatted warmly with O'Neill in the tunnel before the game, replaced Mark Hughes who was sacked last week after 11 months in charge.
The former Portsmouth, West Ham United, Southampton and Tottenham Hotspur manager was strongly linked with the vacant England job this year before being controversially sacked by Spurs in June.
Villa's Brett Holman struck a crisp shot centimetres wide early in the second half and Adam Le Fondre should have put Reading ahead when he sent a free header wastefully over the bar.
The deadlock was broken 10 minutes from time when Benteke rose at the far post to head Ashley Westwood's corner firmly into the far corner of the net.
"Benteke's done fantastic for me," Villa manager Paul lambert said. "He was up against a big lad. It was a fantastic header."
Leaders Manchester United host West Ham United on Wednesday when second-placed Manchester City travel to Wigan Athletic, Chelsea entertain Fulham, Arsenal travel to Everton and Tottenham Hotspur are at home to Liverpool.
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