The Czech Republic international concluded a near £6million move to England on Saturday, and Tare wished him well, adding that they helped the move go through.
"Kozak to Aston Villa? He had asked to go away and we satisfied him by lowering our financial demands," Tare told Lazio Style Radio.
"I thank him for what he gave to Lazio, he is one of the most professional players I've ever known."
Lazio allowed Kozak to leave, even if they failed to bring in their own striker targets, with their main miss being Galatasaray's Burak Yilmaz.
"We tried to the end to bring Yilmaz to Lazio but what happened yesterday [Monday] is very serious," explained Tare.
"His agent made us out-of-the-world requests and so he changed the player's fate. We also had an alternative to Yilmaz, and it was (Juventus' striker, Fabio) Quagliarella but when we reached an agreement with Juventus, coach Antonio Conte stopped the player's departure."