Despite being the frontrunners for much of the season, the Citizens find themselves five points behind title-rivals Manchester United in the Premier League table with just four games remaining.
"There is a lot of pressure on the club now and people expect us to be pushing for all the major trophies," Johnson told The Sun.
"But I think the massive expectations are reasonable when you look at the size and quality of our squad and the investment the owner has put in.
"With the squad we have we should be winning things. It's a season that promised a lot and if we don't win the league now it will invariably be met with massive disappointment."
City visit Wolverhampton Wanderers later today, three and a half hours after United host Everton at Old Trafford.