The Saints manager has made no secret of his admiration for the Villa captain, who he managed at Feyenoord, saying he would "really like" to have him at St Mary's.
Vlaar, who impressed in Holland's run to the World Cup semi-finals in the summer, has just one year left on his deal at Villa Park although the club are planning to offer him fresh terms.
Lambert cast doubt over Vlaar's future when he said he was unsure if his skipper would stay but insisted Koeman should not have gone public.
"I think he is disrespecting when talking about other team's players when they are still their players," he told Sky Sports
"I think that's wrong.
"I wouldn't mind if he picked up the phone, but you don't go public on it
That's the thing that annoyed me the most and the stance is still exactly the same with Ron."
Vlaar joined Villa in a £3m move from Feyenoord in 2012 and helped them to a 1-0 opening-day win at Stoke in the Barclay's Premier League on Saturday.
And Lambert insisted the 29-year-old's performance proved he was not distracted by speculation over his future.
"I don't have a problem
You saw Ron play on Saturday, he was fantastic for us so I don't think anything like that is preying on his mind at all," said the Scot.
"I just thought it was the wrong thing to have done."
Source : PA
Source: PA