The Spurs centre-back had been named in Fabio Capello's provisional 30-man squad but having not played in either of the final two warm-up games against Mexico and Japan, Dawson failed to be included in the England coach's 23-man squad which was announced on Tuesday.
"It was a great honour for me to be involved in the 30-man squad," he has said.
"To end the season and get the call to be involved was fantastic, and a chance to go to the World Cup was a dream.
"Unfortunately the dream was cut on Tuesday when I got a call. It was devastating to get that call, but seven people had to get it and unfortunately I was one of them.
"I was told in a phone call from Mr Capello, he just phoned and said 'I'm sorry, but you haven't made the plane,' but I am in his thoughts for the Euros.
"It was a quick call. I was devastated.
"But, without a shadow of a doubt, it has made me more determined to win my first cap.
"I've always been determined. I was in quite a few squads under Steve McClaren but didn't get a cap then. In the two-and-a-half or three years I haven't been in the squad I've always dreamed of playing for England.
"The dreams have never stopped and they are still there now.
"I was gutted not to get a chance to play in the two games or get a run-out in either of them, that was a big disappointment for me.
"When Sunday night came, I thought it wasn't looking too promising for the World Cup. You never give up hope, but I hadn't played a minute in either of the games.
"I had thought Mr Capello would want to have a look at me, but the manager makes his decision and you have to respect them. I was devastated not to get any time on the field.
"Everyone was working their socks off in training to try and make sure they made it, but he could only take 23 and some people had to miss out."