Published: 2017-12-02 04:03:51 BdST
England have made clear that their dissatisfaction over comments aimed at Jonny Bairstow during their second innings in the 10-wicket defeat in the first test in Brisbane last week that gave the hosts a 1-0 lead in the five-match series.
Anderson compared the antics of the Australians to bullying in a column in a British newspaper but an amused Smith told reporters that when it came to doling out insults in the middle, the England paceman was among the worst offenders.
"I read the article, and it's interesting coming from Jimmy, calling us bullies and big sledgers," Smith told reporters.
"I think he's one of the biggest sledgers in the game, to be perfectly honest with you.
"To me in particular, I remember back in 2010 when I first started and wasn't any good, he was pretty happy to get stuck into me then. Pretty interesting coming from Jimmy."
Anderson took 24 wickets when England retained the Ashes 3-1 in Australia in 2010-11, while Smith managed a high score of 54 not out in three tests over the series.
In Brisbane last week, though, Anderson managed two wickets at the cost of 77 runs while Smith put together a match-turning innings of 141 not out.
Anderson, who also complained to the umpire about Australian short bowling at England tail-enders in Brisbane, said the sledging from the home team had been "infuriating".
"A bully waits until they are in the ascendancy to pounce on people. That is what Australian teams do," he wrote in a column in the Daily Telegraph.
"They are quiet when they are not on top which was the case for the first three days of the Brisbane test and then on day four they came alive. It is down to us to cope with that and deal with it."
Australia have long held a reputation for verbal aggression on the cricket pitch but Smith said he thought the Brisbane match had been played in the right spirit.
"There's a line there that we're not to cross and I thought we played in good spirits," he said.
"I think the umpires and the match referees are there to determine that. From my point of view it's about playing good, hard cricket and I think we did that at the Gabba and I think we'll continue to do that throughout the series."