The 38-year-old was eighth at the British 10,000m Championships and now faces a race against the clock to post the qualifying time ahead of the Tokyo Games.
He finished in 27 minutes 50.54 seconds and will need to go under 27 minutes 28 seconds by June 27 to guarantee a chance to defend his 10,000m titles from 2012 and 2016.
It was a disappointing return to the track for the four-time Olympic champion as he made a comeback for the first time in four years having been focusing on the marathon since 2017.
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. If you would have asked me two weeks ago it would have been a lot different. It’s part of the sport.”
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.
Scott, 27, was born in Northallerton and ran for the University of Tulsa.