Defoe was left red-faced after the t-shirt he wore underneath his Tottenham shirt commemorating his 100th goal for the club was not revealed after he failed to find the net.
"I hope he doesn't wear that shirt again. It's tempting fate," Redknapp said.
"He was unlucky and to be fair to him, he was up half the night because one of his grandparents died on Friday night and was at their bedside."
Redknapp defended his decision to play the former Portsmouth striker so close to his grandparent's death.
"He wanted to play and I'm sure he'd have loved to score against the Hammers because the fans love him there," Redknapp said sarcastically.
"He always gets a good reception and I'm sure he'd like to have put a goal past them."