The Spanish striker's treble – and a second-half goal from Lewis Holtby – led the English Premier League side to the convincing 4-1 win in the UEFA Europa League clash on Thursday.
Villas-Boas said Soldado had never lost confidence despite being without a goal since October, but believes the hat-trick will be a huge boost.
"I don't think he lost confidence but I think as a striker you have to persist in trying to finish off the situations you are given," Villas-Boas said.
"That final touch hasn't been there for him recently, bearing in mind he scored three today this will be a great boost of confidence for him."
Tottenham finished top of Group K after completing six wins from as many games, while Anzhi had already qualified in second leading into the encounter.
Villa-Boas praised his team's professionalism in performing so well despite having progression sealed.
"What pleases me most about this performance tonight was the professionalism of the players and the dedication to the game to give something back to a good house and the fans we had tonight," he said.
"It was important for Danny (Rose) to get some minutes after almost three months and a half of absence and for Christian (Eriksen).
"They will probably need a little more time and training sessions to get back to full fitness but that should happen very soon and with this packed festive period they came in at the right time for us."
Villas-Boas dismissed reports he was considering sending Argentine attacker Erik Lamela out on loan, saying there was 'no chance' of that happening.
He praised the 21-year-old for his performance, saying he was 'extremely happy'.
"It was still not his best we can see but still a good performance," Villas-Boas said.
"He had a big chance on the header and this last shot to brighten a little bit more his performance but I was extremely happy with how he played."
