Redknapp's side required a 72nd minute strike from Kyle Walker to seal the win and Redknapp claims that the scoreline was justified.
"We upped it [in the second half]," Redknapp told Sky Sports News. "We got better and stronger and we took over.
"We deserved the win and I thought in the second half we were excellent."
The three points moved Spurs up to sixth in the Premier League table.