Northallerton’s Marc Scott was overlooked despite carrying the qualification standard in the 5,000m and 10,000m while Pudsey’s Alexandra Bell missed out on the third selection spot in the women’s 800m.
Scott, who competed at the world championships in London earlier this summer, said the selectors had told him he was not considered to be a medal contender.
The 23-year-old, who signed a professional sponsorship with Nike over the summer, said: “I could have appealed but chose not to.
“It was expensive and no one has ever been successful. I know a friend who did appeal but he got rejected. It’s not worth it.
“Training will go ahead and resume as normal, I have bigger things to focus on and specific goals in mind which will be good.
“The World Indoors in Birmingham in March is the main goal now.”
Greg Rutherford, the London 2012 Olympic long jump champion, and Britain’s sprint-record holder, Dina Asher-Smith, will headline the 75-strong England athletics team for next year’s Commonwealth Games.