Spurs won 4-1 on the night, but not before Wycombe had taken the lead.
Winks said, "It's a cold one, so we didn't want extra time!
"It was a tough one. They are a good side and made it difficult for us from the first minute. We expected a fight and we had to go right to the end and thankfully, it didn't go to extra time.
"It's the FA Cup and you never know what is going to happen. We had a lot of chances and opportunities we didn't take but the belief in the team is that we keep going until the final whistle and luckily that paid off for us today.
"I've been working on it a lot after training and when the ball came to me I just composed myself and tried to go for pace rather than lashing at it and seeing where it went. I'm happy to score whenever I get the chance.
"It's difficult not to get regular game time and build up momentum but every time I get the opportunity I have to take it, that's down to me to perform well."