The Three Lions suffered a group-stage exit for the first time in 58 years as Costa Rica's 1-0 victory over Italy on Friday sealed England's fate.
Rooney, who bagged his first ever World Cup goal in the costly 2-1 defeat to Uruguay on Thursday, took to Facebook to convey his disappointment over the campaign.
"Absolutely devastated to be out of the World Cup. Going into each game we had great belief in ourselves but unfortunately it hasn't worked out," he wrote.
"Sorry to all the fans that traveled and at home that we haven't done better...gutted!"
Roy Hodgson's side conclude their Group D campaign by facing already-qualified Costa Rica on Tuesday.