The Black Cats were facing relegation from the Premier League, but managed to claw their way into safety in the latter stages of the campaign.
So far this season, Gus Poyet's men are yet to win a game following three draws and one defeat.
"We want consolidation, no panic, not to be looking over our shoulder every week," The Chronicle quotes Johnson as saying. "We want to go into games playing with a bit of freedom. Not so intense and with so much pressure on us."
Johnson scored his first goal of the season in Saturday's 2-2 draw with Tottenham Hotspur at the Stadium of Light.