Roy Hodgson's men suffered two defeats in their opening two games against Italy and Uruguay to leave them without a chance of qualifying for the second round.
Despite being delighted to represent his country at the World Cup, Lambert has described being knocked out of the tournament as "probably the worst experience" of his career.
"It's a difficult scenario to be in, everyone's disappointed about what's happened and the fact that we've got one more game left," Lambert told TheFA.com. "But we've got to be professional and we've got to give our best and get three points to finish on a high against Costa Rica.
"It's been the best experience of my career and probably the worst experience at the same time.
"It's always difficult being an England fan and getting knocked out, but this time being involved is devastating to get knocked out at an early stage."
England face Costa Rica in their final game of the tournament.