The centre-back was strongly linked with a move to Queens Park Rangers in the summer, and turned down a move to the Hoops after Spurs had accepted a £9m bid.
The 29-year-old has since won back a place in the starting lineup, which has delighted his boss.
When asked if he had made a mistake in trying to sell Dawson, Villas-Boas said: "Yes. I think we appreciate the fact we were able to hang on to him.
"We ended up being on the better side by the fact he agreed to stay with us. We were lucky in that sense."
Spurs host Lyon in the Europa League on Thursday.