The long-distance runner positioned in eighth place at the European Cup 10,000m Championships and now faces a race against the clock to post the qualifying time ahead of the Tokyo Games.
Despite it being his first 10,000m run for four years, Mo Farah was expected to achieve the 27 minutes and 28 seconds needed to qualify for the Games.
Instead, he finished in 27 minutes and 50.54 seconds.
Sir Mo must achieve the 27 minutes and 28 seconds by June 27 to guarantee a chance to defend his 10,000m titles from 2012 and 2016.
Farah, who suffered his first 10,000m defeat in a decade, revealed he was battling an injury to his left ankle but insisted it was important to try to qualify in Birmingham.
He said: “I’m disappointed with the result. The last 10 days hasn’t been great but no matter what I achieve in my career it’s important I come out and show at the trials.
“It would have been easy not to show. I dug in deep and with 15 laps to go, you know my face, I was hurting hard. I had to keep fighting and digging in.
“I’ve been carrying a niggle since I came back from training. It is frustrating because I have done a lot of good work in Flagstaff. If you would have asked me two weeks ago it would have been a lot different. It’s part of the sport.
“It just suddenly came on. I have had some treatment to it and then coming back, it really flared up. To be honest, this is the first bit I have done of track in the last two weeks. It is not ideal.
“What makes us great is being able to challenge yourself and prove it. So that is what you have got to do as the next stage.
“I am four-times Olympic champion but that doesn’t mean nothing. You’ve got to go out there each race and mix it with the best and give yourself a chance.”
Marc Scott, who finished seventh to be crowned British champion, ran under the qualifying time in February to put him second on the UK all-time rankings behind Farah’s national record of 26:46.57.
Morhad Amdouni took the win at the University of Birmingham’s athletics track.
Eilish McColgan, who already had the Olympic qualifying time, won the women’s 10,000m race in 31:19:21 after a fast-paced finish while Jess Judd came third behind Israel’s Selamawit Teferi to seal her place in Tokyo in a personal best of 31:20:84.
McColgan said: “The last kilometre was just an absolute blur. I could not ask for any more.
“My mum (Liz, who won 10,000m silver at the 1988 Olympics) was saying ‘do not leave it to a last lap sprint’ and then I got to 400m and thought ‘oh no, this is a last lap sprint’.”