The Hammers enter their 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."
All eyes will be on Blackpool's team sheet - and manager Ian Holloway admits his players have given him plenty to think about.
The Premier League are investigating Holloway's decision to make 10 changes to his side for Wednesday's 3-2 defeat by Aston Villa but for the Tangerines manager the biggest talking point was how well his so-called fringe players acquitted themselves.
Indeed, they came agonisingly close to snatching a draw after DJ Campbell equalised three minutes from time only for Villa to go straight down the other end and claim the win with James Collins' header.
Many of the players were late summer signings with little or no Premier League experience and Holloway argued they had waited more than long enough for a chance.
He said: "I've got a fantastic problem. That's what I asked them to cause me, by being as good as the other team, if not better. I think some of that team have played themselves into my team, and that's exactly what I wanted them to do.
"They haven't been rewarded well enough. They deserve to play. If that was my kids and an ice-cream, I'd have bought them an ice-cream long ago because their behaviour's been absolutely exceptional. But unfortunately my other kids were doing so well I didn't want to change it."
Marlon Harewood and midfielder Ludovic Sylvestre were among the players that stood out at Villa Park but the one who really caught the eye was teenage winger Matt Phillips.
The England Under-19 international marked his Premier League debut against Blackburn in September with a goal two minutes after coming off the bench and his impact on his first top flight start was no less impressive.
Phillips, who joined the club in August from Wycombe for an initial fee of #325,000, caused Villa's defence all sorts of problems and set up Harewood's opening goal with an audacious back-heel.
Holloway was glowing in his praise of the 19-year-old, saying: "How many other people are going to watch that and think, `I wish we'd bought him'? And that kid hasn't even played yet. I played him at right-back twice and he's not a right-back, he's a winger.
"I thought he was absolutely unplayable at times. Everybody talks about Charlie Adam, soon the name on everybody's lips is going to be Matty Phillips.