The 20-year-old featured in all three of his country's games at the European Championships as Stuart Pearce's squad crashed out at the group stage without registering a single point.
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"The mood was devastation," Wickham told the Northern Echo. "I don't think there are any players in there that are going to be proud of what we have put in. We have let the country down and we have let ourselves down in the tournament.
"I honestly couldn't tell you why it went wrong. I think coming into the tournament we had a lot of confidence. We knew we had strength in numbers but obviously when it came down to it we just weren't good enough.
"For now, it is just back to the club, work as hard as I can and try to get into that Sunderland team. Now obviously there is nothing we can do about this tournament - it has gone.
"For me personally, I am looking to the next one, but first and foremost I want to get back into the Sunderland team and starting to play football again."
Wickham made just 10 Premier League appearances for the Black Cats last season, and was sent out for a month's loan at Sheffield Wednesday in February.