His side scraped through by the odd goal in seven on Saturday, as a plucky Farsley Celtic pushed the Bucks to the very end in the 4-3 victory.
Clubs earn £6,000 if they progress through the first round proper of the competition.
When asked if the financial gain from the competition could be spent on any new charges, the Bucks chief said: "I think anyone is thankful for it really.
"I think with our situation, we are moving in the right direction financially and I think the chairman said that recently.
"Things are great, the community and businesses are re-engaging with us, we are on the up and that money can really help us."
The 452 fans who braved the cold on Saturday, to see the Bucks hold out to progress were treated to an end to end topsy-turvy tussle.
Telford went in front but were pegged back, before five goals in 30 minutes set the game alight.
And Cowan reserved praise for the band of supporters who came out on a bitterly cold afternoon.
He added: "They've been amazing and I keep waxing lyrical about the supporters.
"It was brilliant to have a bit of banter with them behind the dug out.
"They were helping us through it, cheering the team and it is brilliant.
"I would urge everyone else to come and get on board because we are going to have a good season this season."
In recent weeks against Altrincham and Bradford Park Avenue, the Bucks have performed well without getting their rewards.
On Saturday, despite the performance not being as good as it has been, Cowan was pleased his side showed they could win ugly.
He added: "The last two weeks we have come off the back of two losses and played well.
"It wasn't the prettiest of performances, but it was a win and it sets us up nicely ahead of Chester next week."