"I am extremely happy with the way we played today," Verbeek said.
"We played with great control, especially in the second half. It was a very comprehensive win for us. I think the second goal really set us free. For us, the most important thing is that we have three points from this match."
Verbeek was delighted with Kewell's contribution as the midfielder seems to have finally put his long-term injury woes behind him.
"Kewell played a great game, very disciplined throughout the match. It is good to have him in the team," he added.
"I thought even Mark (Schwarzer) had a great game tonight. I think we have done remarkably well in away games despite losing one (to Iraq)."
However, the Dutchman warned that results such as Saturday's will not prove to be a regular occurrence.
"I would like to tell the Australian media that they shouldn't expect 3-0 or 4-0 wins every match," Verbeek said.
"It is not possible so they better not get used to such results. I think we did make some silly mistakes in the match, like giving away free-kicks and corners, but overall I am fairly satisfied.
"In principle, a goal is a mistake and we forced Qatar to make three mistakes which resulted in great goals for us. We definitely scored quality goals."