Johnson hurt himself in training at the end of January, giving manager Roberto Mancini barely any time to find a replacement.
Mancini said: "After Adam Johnson got injured we had a big problem because he is different to the other players. We don't have anyone else like that but he won't be back for another month."
He added: "We are so tired and fatigue is a factor.
"At the moment, we need all the players available because one match every three days, week after week, is very hard.
"But I can't keep the players fresh because we only have 14 players.
"We can't practice. It is not possible to train.
"We prepare for matches but we only have 48 hours to recover. It is a big problem."