The Hammers eventually ran out 5-1 winners over the eighth-placed Championship side - the second-half performance in particular impressing Grant.
"We are the Premier League team so normally we need to win these games, but they are difficult because they are playing well and tactically they are very good,'' he told ESPN.
"But we played well in the second half and it was difficult for them.
"We spoke about this at half-time because the line of the defence was too high. We passed the ball better in the second half and scored the goals.''
And although a cup win does not equate to much-needed Premiership points for the relegation battlers, Grant said it was certainly a confidence-boosting victory for his side.
"We want to win every game. We know in the cup you lose one game and you're out, but in the league there is always the next game to make things better.''