The Fifers were due to play Premiership side Heart of Midlothian in a testimonial for former captain Kevin Smith on Tuesday night.
That game will round off East Fife’s pre-season campaign with the opening game of the competitive season, a home match against League One favourites Dunfermline Athletic, following on Saturday.
Both will provide difficult tests for Crawford’s side but the manager believes they are the kind of opposition his players should revel in competing with.
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“To come into a game against Hearts, that’ll be a test for us and a challenging night,” said the manager.
"Then we’ll train on Thursday night, whether it’s a recovery session, to carry us into the Dunfermline game and think about how we’re going to play against Dunfermline.
"I know James McPake will have them working hard and I’ve been doing my home work on them already.
"It’ll be a tough, challenging League Cup campaign but you want to play against better sides and sides above you to see what their make-up is to stand us in good stead for the season ahead."
Crawford added some more firepower to his team ahead of Saturday’s 3-0 friendly win over Cowdenbeath.
Teenager Ryan Schiavone has joined the club from Hearts and the manager is excited about working with the youngster while also believing the forward will be able to learn plenty from the likes of Alan Trouten.
"Ryan, in terms of developing him as an out and out striker, may take possibly a year or two for him to play the sole role,” he said.
"You can see with Alan Trouten he’s pinning defenders and taking the ball in from the midfield.
"Ryan can look at that.
"But what excites me for Ryan to develop, he can also play in wide areas because he has good legs and works hard going back the way.
"Sometimes as coach or a manager you can have people in the building who want to help so Trouten will be massive.
"It won’t just be on the pitch this year, I’m hearing things during the game in the first half, he was talking to him about his movement and that’s brilliant.”