Neill, who is also the Australia captain, was keen to secure regular first-team football after the Socceroos qualified for next summer's World Cup in South Africa.
The Socceroos struggled in hot conditions as the Qataris went for broke but they maintained their record of not conceding a goal in the final qualifying phase.
They were incensed by what they thought was a blatant attempt to win an early penalty after the CSKA Moscow player went down in the Socceroos area as he tussled with Carl Valeri.
Australia produced a rousing second-half display to knock Serbia out of the World Cup - but it was not quite enough for the Socceroos to sensationally earn a place in the round of 16.
In the end it was a disappointing night for both sides, with the Socceroos left to rue the damage done to their campaign by the 4-0 thrashing they sustained in their opening game against Germany.