The Hammers are entrenched in a relegation battle, having collected just one win from 14 matches, going down 3-0 at Liverpool last weekend.
Striker Carlton Cole labelled the Anfield defeat as "diabolical" and suggested Grant's men should now try "ugly football" in an attempt to get themselves out of trouble.
Extra pressure for a positive result had been added by the West Ham board have designating the clash against fellow strugglers Wigan as the 'save our season game' - with reduced admission prices to help ensure a bumper crowd.
Grant appears, for now at least, to have the support of the owners with David Gold having followed vice-chairman Karen Brady in a visit to the training ground this week.
The Israeli maintains nothing will be decided tomorrow alone, but intends to stay true to the "tradition of West Ham".
"I don't know what is ugly, that we will not shave before? Or that we put the ball in the stand?," Grant said.
"We cannot do it, this is not the tradition of West Ham. It is not something I believe in.
"However, when the game is not going so well, we need to do some different things, especially when we are winning."
Grant continued: "Any game is very important for us, and we want to win the game, but even if we win we have a long way until we say, which I believe we will, that we can do it.
"Even after 20 games, there is enough time to do it, it is not easy of course, but of course it is possible.
"Any gap, especially at the bottom can change.
"I will not say it has been injuries, or the decisions of the referees has been badly, badly against us.
"I want to look at from now on what will happen, and I still believe in this team and this club, this is what is important to me."
Grant indicated he was not impressed by Cole's post-match outburst.
"What I have to say, I will say to the players. I am not dealing with the players through the media," the Hammers boss stressed.
Grant believes his squad, who could have key midfielder Scott Parker back from a chest infection, can actually take strength from their predicament.
Wigan boss Roberto Martinez believes his team are lacking in results only this season.
Martinez is happy with most of Latics' output during a difficult start to the campaign but knows they must start to collect the points he feels they deserve.
Wigan have won just one of their last seven league games and slipped back into the bottom three with defeat at Manchester United last weekend.
They now face a crucial encounter against the Hammers.
Martinez said: "Overall the consistency in our performances has been really good.
"There is only one performance in the last 10 I haven't been happy with.
"As a squad we are getting closer together. We are getting stronger and slowly you can see good signs of the potential of our squad.
"The talent in the squad is huge. I am delighted and extremely proud of every single member of the squad."
Wigan must overcome the loss of striker Hugo Rodallega and Antolin Alcaraz, who are both suspended after being sent off at Old Trafford.
The game also comes too soon for another defender in Emmerson Boyce but club captain Gary Caldwell has an outside chance of featuring after a thigh injury.