Having collected just five points since Christmas, the Londoners are now facing a huge test of their resolve with six more games to come this month including cup ties against Notts County and Shakhtar Donetsk.
Hodgson said: "It is a difficult time and it is going to remain a difficult time.
"What we are going to be doing is trying to work hard and shore up things as best we can in the hope that come March or April some of these players will be returning and we might look stronger.
"We are victims of our own success. We are still in the FA Cup and the Europa League.
"And we had another game against Portsmouth because of the bad weather. We are facing nine games in four-and-a-half weeks.
"But quite frankly we don't really have the squad of those teams and it pushes us more to the limit than them."