Heavily fancied to impress in Poland and Ukraine, the Oranje finished bottom of Group B after losing all three of their games but the midfielder was content with his own personal performance.
De Jong told the club's official website: "The Euros were disappointing for me because we went out in the group stage, but personally I had a good tournament - however, the team effort was not the best."
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Looking ahead to the upcoming campaign, the 27-year-old admits that he is keen to be back amongst his domestic team-mates, adding: "I've already had a few days with the team in Austria, but it's always a good feeling to come back to Carrington.
"The internationals have all come back from the Euros, so it was good to see them as well.
"It's good to be on the pitch again. It's always nice to see the ball again and just to have the smell of the grass and great to get back into training."
And, despite only making 14 league appearances last season, the midfielder understands manager Roberto Mancini's rotation policy.
He continued: "The team is the main thing now. Obviously everybody wants to play for themselves individually, but it’s not always going to happen, because we have a big squad.
"But for the team we just have to go now and try and win as many trophies as we can.
"A lot of teams and a lot of people are going to look up to us after winning the Premiership and we are the team to beat at the moment. But for us as a group, we always keep it calm and we just have to focus on what we do best and that is to play football on the pitch. We just have to do our best."