Having been bested in most departments by the Irish at Murrayfield, four penalties from Greig Laidlaw helped the Scots record a surprise victory to give them an outside chance of claiming the RBS Six Nations crown with two games remaining.
Second-place Wales are the next side to make the trip north of the border when they head to Edinburgh on March 9, looking to build on their 26-9 victory over Italy in Rome on Saturday.
Johnson was delighted with the scalp against Ireland but has admitted they must make big improvements if they are to continue their push for their first Six Nations crown this term.
He told the BBC: "We're still in the tournament - we are in it up to our ears. That's great for the fans and the team but let's not get carried away.
"I've got to be honest, that was not a game (against Ireland) we should have won. But we showed great spirit and great heart - and I love a team which shows great spirit and great heart."