The 19-year old Australian-born left-back made his Premier League debut for the Reds in the weekend's 2-1 loss to Chelsea with former Socceroos star Schwarzer looking on from the Blues bench at Stamford Bridge.
Smith, who has represented England at U17 and U19 levels, moved to the UK when he was 14 and could emerge as a possible World Cup bolter for Ange Postecoglou's Socceroos squad but Schwarzer feels he does not need to make a choice right now.
"He looked very, very sharp and did not look out of place," the Fulham great told Fox Sports of Penrith native Smith.
"I don't think you should use it (World Cup selection) as a carrot though," he added of a possible Socceroos allegiance.
"I think the kid should make the decision based on what he really thinks and it is hard.
"You would like to think he feels very much Australian but in the end it is about what he feels in his heart."
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