Recalling the 2006 Ashes series, Cook said, "I can't really sum up on what he has achieved. As a batsman alone, he's among the best batters I've seen. We just could not get him out in 2006."
The just-concluded Perth Test against South Africa was Ponting's last and the 37-year old's retirement address was held yesterday.
"He hits the ball as cleanly as I have ever seen a cricket ball being hit. As a player of fast bowling, he had all the time in the world," Cook added.
Cook said it was a "privilege" for him to have played against the Aussie.
"He is an unbelievable competitor. I am very privileged to have played against him. I wish him all the best in his retirement," the England opener said.
On Sachin Tendulkar's slump in form, Cook said: "Sachin is a fantastic player, and his records speak for themselves."