The former England keeper somehow clawed away the Scotland international's 64th-minute header on a night when Redknapp saw plenty to persuade him that his cause may not be a forlorn one.
"We worked hard and we deserved a point tonight," said Redknapp.
"We defended well and denied them chances. I feel more optimistic tonight than on Saturday.
"I saw enough to think we can go on a small run and keep ourselves in the pack."
Sunderland gaffer Martin O'Neill added: "I know QPR will be buoyed by Harry Redknapp's appointment, but I thought we could create enough to win."