The entertaining match at the Al Sadd Stadium looked to be heading to penalties after both sides squandered a number of opportunities before Kewell was left unmarked to direct his header home after a beautifully flighted ball from Matt McKay.
Australia, the best FIFA ranked side in the tournament at 26th, will play Uzbekistan in the semi-finals at the Khalifa Stadium on Tuesday.
"The team showed a lot of heart," Osieck told reporters. "Uzbekistan is waiting. They are a good team and they play a very different game."
Iraq's playmaker Nashat Akram struggled to find space in the opening stages under the watchful gaze of Australia's midfield duo of Mile Jedinak and Carl Valeri but the holders came back into the game in the second half.
Iraq's Mohammed Kassid continued to be the busier of the two goalkeepers but neither was called upon to make any difficult saves as both sides proved wasteful in attack as half-chances continued to flow.
As the match entered extra-time both sides continued to press for a winning goal but Mahmood misjudged his header from close range, Ala'a Abdulzehra's toe-poke lacked power and Jedinak deflected Ognenovski's goal-bound overhead kick over the bar.
"Iraq came back very strongly in extra time, I'm particularly happy for Kewell that he got the deciding goal," Osieck said.
"I think we played better in extra time - hard-luck for us, good luck to the Australians - I think it was a very exciting match," Sidka said.
"You saw everything there is to offer in football. The spectators saw a great match. We had many chances, we did everything, in the end it was one cross and one header."
