The Irons host Stoke boosted by last weekend's 3-1 victory over in-form Liverpool, which saw them close the gap on safety to just a single point.
With fixtures against both leaders Manchester United and Champions League hopefuls Tottenham coming up as well as former club Chelsea, Grant could be forgiven were he to prioritise targets.
However, now with the luxury of a near full squad for the first time, the defiant Israeli maintains all opportunities are there for the taking.
"Sometimes I know people lose their belief when they are at the bottom, but we never did it. We were always seeking to do it our way," Grant said.
"I am very happy that we took the points against Liverpool, but now we have a lot of games ahead of us that we want to continue with these performances and to keep winning."
Grant added: "Of course we need to win those games against teams around us, but we will not give up in any game.
"We showed we are a class team against Liverpool, in the beginning of season against Tottenham and in the Carling Cup against Manchester United.
"If we are at our best, we are not an easy team to beat.
"We have a good chance to stay up if we keep playing as we have been playing the last games and taking points."
Grant is not concerned with how the table looks now, only when they come to tot up the points in May.
The Irons boss said: "I know that last year was 35 points, the year before was 38, but the last time West Ham were relegated it was with 42 points.
"It depends because this season there is not a weak team, every team is taking points.
"It will be difficult to predict how many points you need.
"But I am not looking about this because if we do what we need to do, we don't need to look at this."
Demba Ba has certainly made an impact since his January transfer from Hoffenheim.
The Senegal forward - who almost signed for Stoke - has chalked up three goals in as many games, vindicating Grant's decision to push the transfer through.
"I have followed him for a long time in the Bundesliga. He did well," the West Ham boss said.
"He is a kind of player I like, a player with movement, intelligence. He knows how to score goals as you saw in the last games.
"I can tell you that he's not yet at his best."
Stoke manager Tony Pulis believes his side are still trying to adapt to a different style and that is why their away form in particular has been patchy.
He is looking for a change of luck.
Stoke have won only three league games out of 14 on the road and Pulis said: "Our away form has been disappointing.
"A lot of times we have played better than the previous two years but not got the breaks and been unfortunate not to pick up the points.
"It is a tough league and we are still learning. We have played a little bit more open this season. We have (Jermaine) Pennant and (Matthew) Etherington and two centre forwards.
"So we play almost 4-2-4 at times. Although we have done better, especially going forward, we have been a little bit looser at the back and lost goals when maybe when we shouldn't have. It is about getting that balance right."
Both Etherington and Pennant are facing later fitness tests after suffering back and hamstring problems respectively.
Etherington made a cameo appearance in the 1-1 draw with West Brom on Monday while Pennant struggled after the match.
Stoke would appear to be comfortable in 10th place but Pulis is taking nothing for granted in the club's third season in the Premier League.
He said: "The aim has always been to get to 40 points as quickly as we can, especially this year when there are so many clubs close together.
"I have never known the league being so tight. It is exciting for everyone. It keeps the blood flowing.
"In fact I've had some blood tests done. The medical side are pushing on and even check the manager.
"I think (chairman) Peter Coates is doing it just to check that I am all right. I've had a couple of calf injuries. It is old age and sitting in the car driving up and down the motorway."
Source: DSG
