Defoe hammered home a penalty on 67 minutes to create history with his 23rd European goal for the club and moving him one clear of Martin Chivers in the process.
The striker's goal came after Erik Lamela, who finally broke down Sheriff with the opener on the hour, was tripped in the area following a tricky run.
Villas-Boas revealed the squad's delight for Defoe, but hopes they now go on to progress deep into the competition.
"We are all particularly happy for him," he said.
"It is a great honour and will stay in time like Martin's and will be very difficult to break.
"I hope it means this club will continue on this competition in to the later stages to make it even more prestigious for him.
"We were expectant and glad that it happened today [Thursday]. We were trying to put him through on goal, Erik did very well to create the chance through the penalty and he slotted it home."
England international Defoe will harbour aspirations of making Roy Hodgson's squad for next summer's World Cup and revealed he had been told by Chivers at half-time to make the record his own.
"He's a legend," Defoe told ITV4.
"I saw him at half-time. He said to me keep it going you'll get it, it is so nice for someone like Martin to say that."
He added: "It was frustrating tonight, I couldn't really get much space. I just thought to myself stay patient - to go to the top of the list I'm delighted. I was confident, what an opportunity to do it."
Despite Defoe's landmark goal the evening arguably belonged to Argentina international Lamela as he started to show the White Hart Lane faithful the level of ability he possesses.
Villas-Boas had previously said the language barrier and a struggle with adapting to British life had led to the former Roma man's slow start in north London.
But he was at the centre of almost everything good that Spurs managed on an evening that was only slightly dented by Ismail Isa's consolation strike.
"We were waiting for a good performance from him and I think we got it today," he said.
"We have been patient with him and he has delivered with a game in which he had no fear, took people on and created a lot. We saw some signs for what he can do for us and hopefully now he can progress."
Sheriff head coach Veaceslav Rusnac felt his side played well but conceded Spurs were the better team and has backed Villas-Boas' side to go all the way in the competition.
"They played very well to win the game," he said.
"I think Tottenham are the main favourites to win the Europa League. I think we played a great team today and we played to our capabilities.
"We created some good chances at 0-0 and are overall quite happy with the way we played."