Villas-Boas had allowed the centre-back to speak to QPR after accepting a £9million bid for the player in August. Dawson turned down the chance to move to the west London club in order to fight for a place in Villas-Boas' starting XI, but the Portuguese overlooked the England defender for the opening third of the campaign.
The 29-year-old has since worked his way back in to the Villas-Boas' XI, however, starting the club's last seven Barclays Premier League games. When asked whether he thought it was a mistake to let the former Nottingham Forest man speak to QPR, Villas-Boas said: "Yes. I think we appreciate the fact we were able to hang on to him."
The former Chelsea boss added: "We ended up being on the better side by the fact he agreed to stay with us. We were lucky in that sense."
Although Villas-Boas would probably not consider selling Dawson now, he will have to cut one of his centre-backs loose this summer. With Jan Vertonghen and Younes Kaboul both in their prime, and Steven Caulker considered a bright young prospect, it appears 35-year-old William Gallas - who is out of contract in June - is the most likely to depart.
"We won't start another season with five centre-backs," Villas-Boas said. "We have five top central defenders at the moment - a mixture of young players coming through with lots of experience, and then you have such tremendous central defenders as William, Dawson and Younes Kaboul.
"William has been a massive player for us this season. He's a player we trust a lot. Whatever we decide regarding his future, we'll have to wait and see, but we are aware of what a presence he's been for us this season."
Villas-Boas' team face one of their biggest tests of the season on Thursday night when they host Lyon in the first leg of their Europa League last-32 clash.
The Spurs boss has resisted the temptation to field Hugo Lloris against his old club, much to the dismay of Lyon manager Remi Garde, who sold the France captain to the north-London outfit for £12million last summer.
"I suppose it's kind of a regret (that Lloris is not playing). It is for all of us," former Arsenal defender Garde said. "He was very much loved at Lyon. He made a big impression. He was a great guy so it would have been nice to have the experience of coming up against him, rather than just seeing him in the corridor."