Mauricio Pochettino conceded his side needed a slice of luck to book their place in the fifth round and Winks was delighted with the never-say-die attitude amongst the players and fans at White Hart Lane.
"Credit to Wycombe - they were brilliant. It shows our character and spirit to keep going and come back," he told Tottenham's official website.
"It's always great to score a last-minute winner no matter who it's against or what the circumstances are.
"That's what the Tottenham fans are like. They're brilliant and similar to us, they never give up."