Edmund won three matches in qualifying, including 9-7 in a deciding set against Australian Dane Propoggia in the final round, to take his place in the main draw for the first time.
But the 20-year-old from Yorkshire was unable to get to grips with Johnson’s powerful serve on court 22 at Melbourne Park, generating just one break point as he lost 6-4 6-4 6-3.
That sole break point came as Johnson served for the opening set, but Edmund failed to convert it and his American opponent eventually took the set on his fourth opportunity.
The second set followed a similar pattern, with a single break enough for Johnson to take it and double his lead, the 25-year-old winning 77 per cent of points behind his first serve in the match.
Johnson also served a total of 17 aces and broke Edmund twice more in the third set to book his place in the last 64.
Edmund, who will now head to Hong Kong for a Challenger event, said: “I felt I did not play too badly but came up against a very good opponent who was serving very well and I was not quite able to get into his service games.
“There was not much rhythm in the match because it was tough to get into points. My serve has definitely improved but today it came in and out so I need to be more consistent and also work on my returns.
“It’s been a good experience to win three matches in qualifying so I just need to move forward with it and keep improving.”