The reigning league champions fell to a 32-28 defeat at Rodney Parade last Friday, putting a major dent in their play-off hopes.
Johnson's men fell to fourth in the league table, two points about the Cardiff Blues who have a game in hand over all the sides above them.
Johnson admits the Ospreys no longer have control over their own destiny but reckons the Men of Gwent could still have a major influence.
The Dragons face both the Blues and third-placed Ulster in the coming weeks.
"What I will say is that there are plenty of twists and turns to come in this thing yet," said Johnson.
"Things are changing from week to week, but of course it would be great if the Dragons could perform against the Blues and Ulster the way they played against us last Friday.
"Give them credit, they were outstanding. But we know we have to do our bit. We have a couple of games of the regular season left and we appreciate we have to play a lot better if we are to make the knockout games. We need to help ourselves."
The Ospreys have a must-win clash against league leaders Munster in Swansea on Saturday evening and Johnson insists the Ospreys are ready to bounce back.
"We know what needs to be done," added Johnson, whose side conclude their regular-season campaign with a visit to Aironi on May 6.
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