The Bairns will be making their second appearance in a major semi-final in just over a year thanks to goals from Blair Alston.
"We are delighted to be into the semi-finals, this club stands for bringing through and developing their own players and playing a certain style of football," said Pressley.
"I am really proud, that's two cup semi-finals in successive seasons and it shows how we go about our business.
"It's unfortunate after a game like that there has to be a loser, I think Billy Reid and his team were excellent."
Pressley was also delighted to see Alston notching twice after challenging the midfielder to add goals to his game.
"He scored two outstanding goals, in the last few months Blair has taken his game to another level," added the Falkirk boss.
"The one aspect of his game I have asked him to add to his game is goals and he gave me the best possible answer today."