The Hammers enter tomorrow's clash with Blackpool at Upton Park without a league victory since September, a sequence spanning six games.
They sit four points adrift of safety after 12 matches, but Grant remains confident they are on the right track.
"I say to West Ham fans to not just look at the table," Grant said. "When we look at the table we are not happy, but if you analyse the performances of the players, we are very optimistic.
"It's a strange situation because we don't have enough points like we want, but if you analyse our games the spirit is good and the mentality is good.
"The football that we play is good football and in the last two games we scored two goals in both games. Even before that, we played good football.
"I know we haven't taken enough points, but if we continue to play good football and correct a few things, we will win games.
"Sometimes when you are on the bottom of the league, you see a big gap between you and the other teams.
"You see the games and you say to yourself 'We cannot do anything'. But if we continue to do the right things, I'm sure we will pick up points. This is our target."
All eyes will be on Blackpool's team selection tomorrow after boss Ian Holloway made 10 changes to his side for the 3-2 defeat to Aston Villa on Wednesday.
Holloway has threatened to resign should the Premier League choose to fine him and Grant sympathises with his position.
"Ian is the manager and he knows his team better than anybody. He can do anything he needs to for the team," he said.
"In this case, I must say I support him because he knows what he needs from his side.
"Of course, if it was in the end of the season and it affected the results of other teamsBut when it's now, everybody needs to know that he's the manager and he can do what he must."