After the match, Defoe paid tribute to Chivers and praised the performance of Erik Lamela.
"It was a frustrating night as they camped in and gave us no space in behind. I had to stay patient and I am delighted to score the goal and take the European scoring record. What an opportunity to do it, I was confident with the penalty," he told BBC Sport.
"I saw Martin Chivers at half time, he said to me to keep going and I would get the record. He's a legend.
"Erik Lamela was fantastic tonight. He is strong, good on the ball and it is difficult when you come into a club at a young age. But he made things happen for us, I'm delighted for him."
The win means that Spurs have qualified for the knockout stages.