Soldado scored twice early on before adding his third from the penalty spot as Spurs eased to a 4-1 win and maintained their 100 per cent record in Group K.
Lewis Holtby was the other man on the scoresheet for the hosts, who had seen Almeida Santos pull one back for Anzhi, but it was Soldado's form which had Villas-Boas in good spirits.
"It was extremely important for him to get back to scoring," the Portuguese said.
"I'm extremely happy for him. He's been waiting for a moment like this and it finally happened tonight with a hat-trick. It will be major boost for a player who has been very professional and deserve the respect.
"I don't think he lost his confidence but, as a striker, you have to persist and persist; finishing off the situations you are given and that final touch hasn't been there for him recently. It will be a great boost of confidence for him, bearing in mind he scored three today."
Liverpool are the visitors to White Hart Lane on Sunday as Spurs return to Barclays Premier League action but Villas-Boas said Defoe, who had started the past two games ahead of the Anzhi match, remains in contention to return.
"We have to think about it," he added.
"It's a bit premature. We always wanted to give this game to Roberto after two games in a row for Jermain, who was deserving his chance as well. Now it's about putting the best possible strategy of the game and seeing what we can do.
"What this will help is put the player back with confidence with his final touch and a striker always lives off goals so it's extremely important."
Progressing as group winners means Spurs will miss the best of the Champions League teams dropping down in to the Europa League for the knock-out stages.
But tricky ties could still be found if they are drawn against the likes of Juventus, Ajax, Lazio and Porto, with Villas-Boas not wanting to return to face his former employers.
"It is possible," he said on a potential clash with Porto.
"On a personal level I wouldn't like that. Our aim is to go all the way to the final and I wouldn't like that.
"I have tremendous gratitude to the club and I'm a great fan so hopefully that doesn't happen until the final."
Anzhi head coach Gadzhi Gadzhiev was pleased with his side going forward but felt they could have done more to stem Tottenham's attacking threats.
"We played well in attack but not so well in defence and we were generally too slow to catch the opponents effectively," he said.
"It was an interesting game for the fans and it was an obvious advantage for Spurs to score in the first minutes, this helped the hosts put themselves in a good position."