Defoe went into the game with 99 Spurs goals to his name, but he failed to reach the century mark after missing a host of good opportunities in a frustrating draw that means Spurs are now two points behind Chelsea in the race for fourth.
"Jermain was up half the night due to a family bereavement," Redknapp said. "I wasn't sure whether to play him but he wanted to. He had some good chances today, the little fella, and he normally scores them but it was just one of those days. It wasn't through a lack of effort."
He added: "He was bright, he was sharp he just couldn't score but that's football. That's how it goes, another day he'll go and bang a couple in.
"The two goals he got at Wolves, he had no right to score them. They weren't even half chances."
Tottenham rattled the woodwork three times in total and were wasteful at times in front of goal.
But they also had to contend with some fantastic goalkeeping from Robert Green, who tipped Gareth Bale's late free-kick onto the bar when it seemed impossible to stop the ball going in.
Redknapp was proud of his side's performance, though, and insisted that people are getting carried away with their expectations of his team now that they have made the Champions League quarter-finals.
Redknapp, who was boosted by Bale signing a new four-and-a-half-year contract, insists that Spurs remain on course to win the title in the near future with him, but admits finishing in the top five this year should be considered a fantastic achievement.
"I love the way we play football and I will go home satisfied tonight," he said. "We just could not get a break."
Source: PA
Source: PA