The 52-year-old coach admits the players have been left hurt and disappointed by their FA Cup exit but he insists there is no panic within the club.
"I know that at Chelsea, like a lot of big clubs, every loss is a crisis but it's not like that," said Grant.
"We're a big club. We know how to behave inside after winning and after losing games.
"We are very disappointed to have lost on Saturday, even if we're in good company with the other clubs in the Premier League who have gone out. We wanted to win that game.
"I'm not under any more pressure than I was before, and I'm not under any less. Any loss at Chelsea is like a World War.
"But you can look at it from a negative side or from a positive one. I've spoken with the players. They're very disappointed. I told them I took the responsibility. They said they took the responsibility also.
"After losing in the Carling Cup we won two games, one with a great performance with 10 players. Then Barnsley. We've analysed it, and we want to be as consistent as we were before.
"We were the only team of the four big teams to reach the final of the Carling Cup. Now we're in the same company with the other big clubs in not reaching the semi-finals of the FA Cup.
"That happens. We can only look at the championship and the Champions League. We're very proud with what we've achieved so far.
"The players were very hurt. They're very proud, and it was embarrassing losing a game like that.
"But it doesn't happen very much for us. We've won 80% of the league and Champions League games. In the cup, you can't fix it if things don't go for you. You're out.
"I want to win a trophy this season. I wanted it before. The pressure to win trophies is better than the pressure at the bottom of the league. I don't want that. This is a good life.
"We need to be more consistent but, sometimes, when you change to a different style of football there are problems in the way. I never enjoy losing, but I still enjoy this."