The Three Lions face Montenegro on Friday needing just a point to qualify, although Parker has said that they will try to win the match, so they can then concentrate on next year's tournament.
"We all know that we're sitting here thinking the true test will come at tournament level," Parker said.
"The last time we qualified pretty well and South Africa didn't go anywhere near to plan.
"We always seem to qualify well and now we need to try and replicate that at tournament level. We certainly need to do a lot better than we did in South Africa."
England lost 4-1 to Germany to go out in the second round of the 2010 World Cup.