According to the BBC, Security around the Wales team is to be reviewed after opposition fans ran onto the pitch and approached Gareth Bale at their World Cup qualifier in Macedonia.
It happened as the world's most expensive player, who did not play in the 2-1 defeat, warmed up at half-time.
The Football Association of Wales (FAW) said the team took its own security staff travelling abroad but the host country was responsible in the stadium.
A spokesman said the FAW would be reviewing player security.
Cardiff-born Bale became the world's expensive player when he signed for Real Madrid from Tottenham for £85m.
He travelled with Wales for Friday night's match in Skopje but with his match fitness an issue, manager Chris Coleman decided not to play him. The defeat ended Wales' slim hopes of qualifying for the World Cup.
But as Bale warmed up at half-time he was approached by two Macedonian fans who then appeared to try to hug him before he pushed them away.
The FAW said its security for players was very good but a spokesman added: "Security within the stadium was up to the Macedonian authorities so they should have prevented the fans going onto the pitch and up to Gareth like that."
He said the same thing could happen at away games in future, such as the forthcoming match in Belgium next month.
He added that the team, which has several high-profile players in addition to Bale including Arsenal star Aaron Ramsey, always took its own security staff when travelling abroad, but said having the world's most expensive player among the squad was "new territory" and the FAW needed to adapt to it.
The spokesman said that in Skopje hundreds of people had gathered just to catch a glimpse of Bale.
"It was not just the fans, but it was radio and TV people wanting access... everybody wants a picture of him," he said.