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The four-time British champion was at the Manchester Regional Arena last night to try and secure a spot on the team ahead of Sunday's (27 June) deadline.
The invitational race had been arranged after Farah failed to qualify during the 10,000m trials in Birmingham earlier this month.
Farah, 38, needed to come in under 27 minutes and 28 seconds, but he ended up clocking a time of 27 minutes and 47.04 seconds.
This means he won't be able to defend the Olympic 10,000m title he won in 2012 and 2016 as Team GB heads to Japan next month.
Following the disappointing attempt, Farah said: "You go out there and give it all and that's all you have. It's quite windy. I tried to push and push and I ran my lungs out.
"That's all you can do as a human being, give it your all. I've had a wonderful career. I'm very grateful. That's all I had today."
Farah, who has been battling an ankle injury, said he needs to consider what the future now holds for him, admitting he'd expected to make the grade.
He said: "I don't know what to think or what's next for me. I just have to have a chat with my team and see what's next. If I can't compete with the best, why bother?
"There's no excuse in terms of conditions, it is what it is. I genuinely thought I'd come out here, get the time and then go back to the training camp.
"I've had some decent sessions since my little niggle (ankle and foot) but I thought I should be able to run that. I've always said if I can't compete with the best I'm not just going to go there to make the team.
"I've had an amazing career, thinking about it tonight it's a bit shocking and I don't really know what to say.
"I'm lucky enough to have so many medals, I'm one of these athletes who, if you can't compete with the best, why bother?"
While the time of 27 minutes and 47.04 seconds wasn't quick enough to qualify for the Olympics, according to the BBC, it is a stadium record at Manchester Regional Arena.
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