Wigan substitute Mauro Boselli failed to convert a penalty for his side when they were 2-0 down before Tom Cleverley scored a late consolation goal for the third-from-bottom visitors, who are just two points ahead of West Ham.
"It was a good win and a convincing victory, I am happy for us and hope it is only the beginning," said Grant.
"We played like we have all of the other games, but were more efficient [against Wigan].
"We won, this is the difference and this is the name of the game.
"We started a bit nervous, which you can understand from our position in the league and the last game [when we lost] at Liverpool.
"But the players always tried to do the right thing, were fighting and they have responded.
"We are trying to build a good mentality, which is important."
Grant also dismissed speculation concerning his own future at the club following the poor start to the current campaign.
We just weren't ourselves, and that is where the work is going to be
Wigan boss Roberto Martinez
"I never think about myself, I am in a job where there are always rumours," said the former Chelsea and Portsmouth boss.
"I just need to concentrate on my job, that is what I have done all my life and will do in the future."
The Israeli brought in Wally Downes as his defensive coach this week and, although there are rumours former Hammers favourite Paolo Di Canio could come in as a coach to the strikers, Grant said no approach had been made to the Italian.
He added: "There have been a few names, but I did not speak with him.
"We want to build West Ham step by step and are looking for more specific coaches which will do specific jobs.
"For me, Di Canio is always welcome at this club. He is very respected and I had the honour to see him playing a few times, he was a great player.
"If he can teach our players how to play like him, I will take him!"
Wigan boss Roberto Martinez was left to rue the manner of the goals his side conceded as he believes his players failed to do themselves justice.
"We conceded three very cheap goals for our standards, and that is something we will work on," said Martinez.
"We had a few players missing, but that is not an excuse. You got the feeling nothing was going our way.
"There was a good opportunity to get back into the game with the penalty, and then even at the end we got a good goal ruled out.
"It is quite clear to me the things we need to work on, but I was pleased with the reaction towards the end.
"It was a day of a real test of character, and that was there, but in football you cannot concede cheap goals, otherwise you are making things very difficult.
"We just weren't ourselves, and that is where the work is going to be."
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