The Newcastle shot-stopper made 14 stops during the course of the Magpies' 1-0 win at White Hart Lane, the most by a goalkeeper since the 2006-07 season
Spurs were defeated by Loic Remy's 13th minute goal but denied an equaliser by a fine performance from Krul, who made 14 saves over the course of the 90 minutes.
The Portuguese was disappointed in his team's first half showing but paid tribute to the Dutchman's heroics.
Villas-Boas told reporters: “It was difficult to take. We have to look at ourselves and recognise that our first half was very, very poor. That was the negative, the positive was that we reacted so strongly and I think that the result was unfair, particularly after the second half.
“Tim Krul was the difference. It was a good start by Newcastle and a poor start from ourselves. We responded with a good second half but that 45 minute advantage was the blow for us.
"Our disappointment comes from that but I still think if one of those opportunities had gone in we’d have won the game."
Newcastle raced out of the blocks, seizing the advantage as Yoan Gouffran threaded Remy in on goal for the only goal of the game and Villas-Boas was happy to concede that Alan Pardew's side deserved their lead.
He added: “We must give merit to the opponent. Sometimes things like this happen. Just going into the game you’re focused and do a good warm up and then things in the game don’t happen for you.
"The opponent is there and has merit, brighter start than us that gave them the 1-0 advantage that paid off for them. Merit for them as well but we were extremely unlucky today."
Spurs mustered 31 shots on goal and created a host of clear-cut chances, but Krul secured the three points for a Newcastle team on the up following their 2-0 victory over Chelsea last weekend.
“It was amazing [Krul's display], the decisive part of today’s game," Villas-Boas insisted.
"Last season he had a great game against us as well. He was the inspiration; he made the difference. With a bit more luck we would have found the finishing touch."
The result leaves Spurs in sixth position, while Newcastle move to within three points of the north Londoners in ninth place.