Ahead of tonight's Carling Cup tie with Hull City, Grant said: "I think I have the backing of the players. I can only judge them by their actions or by the words they speak to me.
"I spoke with the players individually and even before I became a manager. My relationship with them is good and I enjoy working with them. You saw on Sunday their attitude was at a high level.
"In training and on the pitch I think Chelsea can be very proud of these players. They are very professional and have a good attitude, I don't see one problem so far.
"But look, I don't think anyone is happy from this situation. The situation has happened but nobody in the club was happy. But it has happened and this is football, it is not the first time it has happened.
"But we need to adapt to it as soon as possible, and I think all of us, the players and the management have done that and we are looking forward to improving our quality of football, that is our goal.
"I am very happy with their attitude, even from the injured players, they all want to play.
"Didier (Drogba) started training on Monday, one week before we expected, Ricardo Carvalho started training on Tuesday and Frank Lampard is doing very well, so I expect to see them in the team soon."
Grant has spoken to most of the players, both individually and as a group, and he has been heartened by the reaction so far. But he knows that in a squad of 25, he knows there will always be someone who is a unhappy.
Grant added: "It has been much better than I thought and I am sure it will be much better from now. When you have 25 players in the squad it sometimes happens that one or two are not happy.
"For the moment, I have not seen that. I am a very positive person - I like to think about the positive things the players can bring to Chelsea.
"I know some will not be happy because I know it cannot be 100% happiness."