Ally McCoist's men reached the fifth round after goals from Nicky Law and David Templeton secured a 2-0 win over Falkirk on Saturday.
McGrandles was part of the Falkirk side, but the 18-year-old midfielder insists he was more impressed with Aberdeen, who knocked the Bairns out of the League Cup with a 5-0 thrashing earlier this year.
Mohsni brushed off the youngster's opinion and admits Rangers are keen to prove they can compete with the top sides in Scotland.
"I'm not going to have an argument with some player," he said. "I think he was upset with the defeat. When you are upset, you say some rubbish stuff.
"Of course I can say to Celtic they won't win the cup, or I can say that to Aberdeen. But it doesn't matter. We will see what happens.
"It is up to us to show we can win the Scottish Cup."
Rangers set a club record 19th win in a row with a 6-1 thrashing of League One rivals Forfar on Tuesday.
But Mohsni insists the players are thinking only about winning the title and not about completing the league campaign without a defeat.
"At Ibrox, we can beat anyone," he said. "It won't be easy but we have the upper hand because the other sides are not used to the big pitch and the big crowd.
"Motivation isn't an issue. We just need to concentrate. We want to win the league as quick as we can. We're not thinking about records, just winning the individual games.
"I didn't even know we had beat the record until the manager told us after the game. It's great because we're now part of the history of the club.
"It would be great to go the season unbeaten but that's not what we are concentrating on, only each game as it comes."