Strachan has been accused of linking racist abuse with the convicted sex offenders’ situation while appearing on Sky Sports’ The Debate programme.
Johnson has recently been released after serving three years in prison for engaging in sexual activity with a 15-year-old fan, and the ex-England winger has not ruled out a return to football.
Strachan said: “If he goes on to the pitch and people start calling him names, have we got to do the same as it is to the racist situation?
“Is it all right to call him names now after doing his three years – have we got to allow that to happen?”
In a statement issued through Press Association Sport, Strachan said: “Given the response in the last 24 hours to a point made on The Debate programme on Sky Sports from over a week ago, and having reflected on it personally, it is important for me to address the issues that have arisen.
“In no way did I intended to confuse or conflate the very serious issue of racism targeted at footballers with the potential verbal abuse towards a player who has been convicted of a sexual offence.
Strachan is an occasional contributor to the programme but Press Association Sport understands he will not be used again.
“Having reviewed the particular segment in light of the reaction, I fully acknowledge that the imprecise use of language in my initial response has left open a perception that should easily have been avoided. For that I sincerely apologise.
“I should have communicated my point more clearly and without the need to refer to the earlier discussion, during which I was clear in my condemnation of the racist abuse which continues to blight football.