Brian Graham’s solitary strike was enough to defeat Dumbarton in the replay at the Strathclyde Homes Stadium.
But Rae said: “The last few years have hit us hard and we have suffered from dwindling attendances. I am not sure what the Celtic tie will bring in, but any money will go to balancing the books.”
Grady, meanwhile, was delighted with his side’s success. He said: “They don’t come much bigger than Celtic so this is a fantastic opportunity.”
Sons boss Jim Chapman said: “I am proud of my players’ efforts, but now we will concentrate on our Second Division campaign.”
Meanwhile, Clyde gaffer John McCormack is hoping his side’s hard-fought 1-0 Second Division victory over Arbroath can act as a springboard to success in tonight’s Broadwood Scottish Cup clash with Livingston.
Cowboy fired: “It was vital we got the win against Arbroath to avoid becoming detached at the foot of the table. Now we have given ourselves a platform for tonight. Livi may be a full-time side, but it is a cup-tie, and if we show enough passion and commitment we will give ourselves a chance.”
In the Third Division, Albion Rovers battled back to claim a 2-2 draw with Forfar after an injury-time strike by Pat Walker kept them just one point off the play-off pace.
Rovers boss Paul Martin said: “Credit to the players. They never gave up and got their reward. But, overall, I was very disappointed with our performance.”
Queen’s Park boss Gardner Speirs was shell- shocked by his side’s 3-1 defeat at Annan.
He said: “I just didn’t see that coming.”
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