"It was as expected - they're ruthless over here," foxsports.com.au quoted Lyon as saying.
"I've had two Ashes tours and a one-day series over here and haven't experienced anything else. They're ruthless and there's not much love. They haven't changed their lines in the last 12 months," he added.
Both Smith and Warner, playing their first match in England after serving their one-year ban for involvement in the Cape Town ball-tampering row, were greeted by boos at various stages of Saturday's game from the 11,540-strong Southampton crowd.
There were audible boos, jeers and chants of "cheat", something which Warner and Smith will need to get used to during the course of the World Cup and also the Ashes Series which is scheduled from August 1.
However, both the batters didn't seem to bother much about the smattering of jeers they were greeted with as Smith scored a match-winning 116 and Warner made 43 in Australia's 12-run win over England.
After the match, Smith also insisted that he tries not to pay attention to the crowd and focuses only on his game.
"I heard a few things as I went out to bat, but it didn't really get to me," Smith said in the post-match press conference. "I'm just trying to keep my head down and move straight ahead and just do my job."
The former Australia skipper said as long as he had the support of his teammates, he didn't get bothered by the reaction of the crowd.
"It doesn't bother me. It's just doing my job and I know that I've got the support of my teammates up on the balcony and that's the most important thing," said Smith.
"If I can make them proud out in the middle and make Austral proud as much as I can well that's my job," he added.
( With inputs from IANS )