The Wearsiders followed a 2-2 draw at the Etihad Stadium with a 2-1 victory at Stamford Bridge to help boost their chances of remaining in the Premier League next season.
Although they remain at the base of the table, they are just three points from safety with a game in hand on each of the three teams immediately above them.
Three of their final four games are at home - against Cardiff, West Brom and Swansea - plus an away trip to Old Trafford.
And Johnson said: "There are still a good few teams who are still right in it yet.
"We said after the Chelsea game, there will be a few teams above us now thinking 'Oh no'.
"If I put myself in their position, after the result came in on Saturday evening, I'd be thinking, 'It's just got even tougher'.
"We have definitely given everyone a scare now and the momentum should be with us.
"With three home games, we couldn't really ask for a better run-in, three home games against teams in and around us."
Watch Sunderland v Cardiff live on Sky Sports 1 at midday on Sunday.