Burnley boss Kompany 'was studying Postecogolou before Yokohama'
The Clarets host Spurs in the third round on Friday night.
Kompany said: "To be brutally honest, it is the best possible draw. You can have these kinds of draws in the quarter-finals, when you have done X amount of games (to get that far) and you have played against League Two clubs and League One clubs. It is better to have the outcome of these games early, for us.
"Game one - if you win the game you can hope for a positive cup run and carry on. If you don't win the game then you move on back to the league.
"I am embracing the challenge anyway, but I am not saying it is a bad draw. It is the right draw at the right time.
On Spurs manager Ange Postecoglou (58), he also said: "I have (been aware of Ange Postecoglou) for a long time - before he even got to Japan.
"Via another person, I got in touch to find out what his ideas were about when he was in Japan. So I am not surprised (by Postecoglou's success).
"He has also done probably the hardest way to do it. He's come from Australia - it's hard to get out of Australia, but he has gone to Japan, Scotland, then getting into the Premier League, eventually.
"With his character and his personality - he can show you in many moments as to why he has become successful without having to be talking about football. You can just see it when you see the person."
