Defoe scored from the spot after 67 minutes to take his tally in European competition to 23 on Thursday as Tottenham booked its place in the last 32 of the Europa League with victory over the Moldovan side.
Erik Lamela had given the hosts the lead on the hour mark before Defoe's spot kick put Andre Villas-Boas' side in command.
Forward Ismail Isa pulled one back for Sheriff, but the plaudits belonged to Defoe, who overtook the mark set by 1972 UEFA Cup winner Martin Chivers.
"It was a frustrating night as they camped in and gave us no space in behind," Defoe told ITV. "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.
"I saw Martin Chivers at halftime, he said to me to keep going and I would get the record. He's a legend."
The 31-year-old also reserved praise for Lamela, who scored his first goal for the London club with a smart low finish.
"Erik Lamela was fantastic tonight," Defoe added. "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."