The Welsh outfit go into the game at Upton Park as the underdogs after Jack Collison's brace in the first encounter at the Cardiff City Stadium. However Mackay insists that his side are still in the tie.
"Most people may now expect West Ham to make it through to the final - that could be a natural reaction I suppose," Mackay told Cardiff's official club website.
"But myself and the team don't subscribe to that. We go into Monday afternoon trying to win the game.
"We have 90 minutes to score twice and, beyond that, to win the game. Right now we have a fighter's chance."
West Ham host Cardiff in the second leg of the play-off semi-final on Monday night.