Mata is currently out of favour under Chelsea boss Jose Mourinho, with the Spain international left under no illusion that he will have to change his game if he wants to win back his place at Stamford Bridge.
Villas-Boas said Tottenham, who face Chelsea at White Hart Lane on Saturday, enquired about signing the playmaker, but were rebuffed in their efforts to get him to move across London.
"We did not pursue it to be fair," Villas-Boas told reporters at Tottenham's training ground.
"When top players become available when their situation changes at a club, particularly for a player like Juan Mata, you enquire about the situation, but nothing went further than a simple enquiry...
"It is normal, last year we were fighting for the same objectives in the beginning the title and after that Champions League qualification, so I suppose after that they did not want to strengthen a rival.
"I suppose it is a sign of evolution from Tottenham as well."
Chelsea also sought to scupper Tottenham's transfer plans by poaching Brazil international Willian from under their noses, signing him after he had undergone a medical in north London.
"I have no idea what motivated them to sign Willian, but I am sure he has strengthened an already very good squad," Villas-Boas added.
"In the end, everybody agrees in that sector they are very strong already, but they decided to do that and he is such a young talent with so much potential that he can always compliment them."