Rovers travel to Ibrox hoping a fifth successive clean-sheet in this year's competition will secure them a place in the last four at the home of their weekend rivals.
The spotlight of the country's media has now switched to the Coatbridge side and Ward believes the intensity of the situation is rubbing off on the players who are desperate to be involved in the 'game of their lives'.
Speaking to Sky Sports News he said: "This is a massive occasion for the club as a whole and a great opportunity for our players to showcase what they are capable of.
"This week has been very difficult for me from the point of view that once the international games were over the media hype around this game began to crank up. Trying to juggle my day job, training and everything that comes with this game has been very difficult.
"But throughout it all I could see the intensity of training moved up a level or two with people trying to push their case to ensure they are involved in the starting XI on Sunday."
And Ward leapt to the defence of the runaway League One leaders who, despite being unbeaten in the league all season, have come in for criticism from some of their own fans for the style of play on the pitch.
"We face a massive challenge against Rangers," he said. "People are quick to criticise them but they have got to this situation because they are unbeaten and have conceded the fewest goals in the league.
"They are in a national cup quarter-final and are also in the Ramsdens Cup final and they have a very experienced squad of players who will make it a very difficult game for us.
"That said, for us to get to the semi-finals would be beyond everyone's wildest dreams. However, it is achievable given the fact that we are only 90 minutes away from it."
Watch Albion Rovers take on Rangers live from Ibrox at 3.00pm this Sunday on Sky Sports 1