Costa Rica's 3-1 win over Uruguay means that England may need to beat both of those sides if they are to qualify for the latter stages, but Hodgson is optimistic about achieving that feat.
"The fact is that if you lose the first game you probably have to win the next two," he told reporters at full time.
"The teams you play against have to win as well, but there is no way you can drift into the second round.
"Italy have the best start, as have Costa Rica, and we and Uruguay are on the back foot. We now play Uruguay and Costa Rica, so at least our fate is in our hands."
Hodgson's side face Uruguay on Thursday night.