The Blues failed to take advantage of Manchester United's defeat at the hands of rivals City earlier today.
But Michael Ballack's glaring miss 10 minutes from time also played a part in Chelsea's inability to end the stalemate.
Grant added: "We are not happy. We want to win every game but especially at home. If we don't win we are disappointed.
"You could say it is a missed opportunity, but it is not easy to play against Liverpool. They are a very tactical team. They don't give you much space to play. In the first half we didn't play quickly so it was much easier for them.
"We were better in the second-half but we missed a big chance at the end. It was a penalty when I saw it at the time and now I've seen it on TV, it was a 100 per cent penalty.
"He is a good referee but he has made a mistake. It has happened. For us it is not the first or second time this season, so we are used to it but he is a good referee."
It was Chelsea's second straight draw after last weekend's 1-1 stalemate at Portsmouth.
"If we draw twice we are not happy but we are still in the chasing pack," Grant claimed.
"I think it has been a big physical pressure on a small group of players in the last two months. So maybe they are a little bit tired but this is part of the game when you belong to a top club.
"They have done a good job until now. It was not an entertaining game that is for sure. We tried to play football but it was not easy today. It is the game we haven't scored in for a long time."
