"We are working as a team to try and reach the finals of this competition and hopefully the fans are not going to spoil it," the England captain said on Monday.
"Respect has to be shown to the opposition. Booing the national anthem is disrespectful. Racism and jumping on the pitch has definitely got to stop.
"It's going to get us in a lot of trouble.
England's Football Association have been fined and warned about the future conduct of supporters after racist abuse, two pitch invasions and 95 arrests marred a European championship qualifying victory over Turkey in April.
UEFA's outgoing chief executive Gerhard Aigner warned of "extreme measures" if the scenes are repeated.
"England fans -- just get behind the team and do it in a nice way, because we deserve it. We don't want to be eliminated from the competition," added the Manchester United midfielder.
Beckham will miss Tuesday's friendly against Serbia and Montenegro in Leicester and the qualifier against Slovakia at Middlesbrough on June 11 through injury and suspension.
