Cole will take a couple of weeks off before deciding his next club move.
Asked whether he wanted Capello to stay, Cole said: "He's a great manager and we've got great players but there are issues we need to address.
"I don't want to go into tactics. I'm just disappointed and apologise to the England fans who travelled out here. We tried our best but it wasn't good enough. We had such high expectations. We wanted to win the tournament and we didn't do that."