A spectator was heard shouting "Get off Warner you cheat".
There were more boos as Warner walked off after being dismissed for 43 to be replaced by Smith, coming in with Australia 82 for two in the 17th over.
Smith played a brilliant innings of 116 off 102 balls and he was out in the penultimate delivery of the Australian innings.
There were a few chants of "cheat, cheat, cheat" when Smith arrived, although a lone Australia fan shouted back "Get 'em Stevie!", according to BBC.
But when Smith reached his fifty, the applause outweighed the boos but the jeers were very much audible. He was booed again when he reached his hundred in the 48th over.
Asked about the boos after the Australian innings, Smith said, "I'm pretty chilled, everyone is entitled to their opinion. I'm just happy to be back playing and doing a job for my team. I fortunately was able to contribute for the team."
Reigning world champions Australia are set to be in England for more than four months in a tour featuring both the World Cup and a five-Test Ashes series.
(With PTI inputs)