Johnson, 30, apologised to fans for unkind Twitter exchanges in the wake of United's 3-0 loss to Real Salt Lake.
The loss was DC United's second straight in the league, leaving them two points adrift of Eastern Conference leaders Sporting Kansas City.
They face the similarly out-of-form Colorado Rapids on Sunday, but coach Ben Olsen faced plenty of questions about Johnson from media on Tuesday.
Olsen said he met with Johnson, but refused to go into detail about what was said.
"Eddie and [my] meetings are going to be our meetings, between us," he said.
"But he's got to react better to things that don't go his way. I love the guy, but he's gotta get better in a lot of areas.
"I don't know a lot about [social media]. I don't go on there. I did hear a little bit about it. I think that stuff is unacceptable as well."
Consecutive losses have been a missed chance for DC, who failed to capitalise on back-to-back slip-ups by Sporting.
Sporting face a tough clash against third-placed Toronto on Saturday, and it could end up being another chance for DC to climb to the top.
In a top-of-the-table Western Conference encounter, the first-placed Seattle Sounders travel to Real Salt Lake on Saturday.
Only two points separates the leaders, but the Sounders have two games in hand.
On Friday, the Houston Dynamo host the Philadelphia Union in a clash between two teams chasing play-off spots.
Will Bruin, the Dynamo's leading goalscorer with eight this season, is likely to miss due to an ankle injury.
The struggling Montreal Impact are still looking to break their losing league run – which stands at seven – when they host the Chicago Fire.
The New England Revolution and Portland Timbers do battle, while the Los Angeles Galaxy visit the Columbus Crew.
Chivas USA host the Vancouver Whitecaps and the San Jose Earthquakes meet Dallas FC.
