Johnson played in the last Grand Slam-winning side in 1995 - but since then England have fallen at the final hurdle three times, most recently at Lansdowne Road in 2001.
Coach Clive Woodward has highlighted the fact that this crop of players, currently rated the top team in the world, deserve a Grand Slam to mark the achievements of recent years.
But Johnson said: "I don't think we are owed anything. We probably should have won one, but you don't get them handed to you."
The giant Leicester lock acknowledges the pressure England are under - but he claims the Irish side will carry even greater expectations as they attempt to deliver only their second ever Grand Slam, 55 years after securing their first.
"There's pressure on them as well as on us. They're at home trying to win a Grand Slam for the first time in however many years, while we are trying to win one again after slipping up in the last three or four years.
"It's going to be a hell of a struggle on Sunday to win. I think this is the best Ireland team we have ever played against, in terms of being consistent and winning games.
"We are not expecting them to play with anything other than the commitment and the skill they have played with all season. We don't expect them to freeze or to let the pressure get to them.
"If anything we expect it to be the other way round. We expect them to be the most energetic and enthusiastic they have been all season - but we also plan to be like that."