The Gers roared back from a 3-1 deficit in normal time to force extra time, which was headlined by a crucial penalty save from Jenna Fife on Saoirse Noonan.
Fife then made herself the hero in the shootout as she saved two Celtic penalties, and Rangers went four from four, to book their place in a fourth successive final in the competition.
Speaking to RangersTV after the triumph, the Head Coach commented: “I’m really proud of my players. It was drama from the get-go and I don’t think I’ve ever watched or experienced a game like that.
“You probably feel like you have such little control over it, which is a frustration. I don’t think the performance levels for us today were anywhere near where we want it to be.
“I know cup ties have the potential to throw that at you because it’s an all or nothing type game. It was a crazy course of events, but I think the resilience is the biggest thing from the group today.
“The most pleasing and satisfying bit is that we were never out, even when it looked like we were gone. We kept fighting back and overcame tough moments within the game. I’m just so pleased for the group.”
On Fife’s heroic performance, Crichton continued: “It wasn’t even just the penalties; she had a few big, big moments. She put her body on the line.
“I know she’ll be disappointed with the second goal. She probably felt she could have done a bit more when she came out, but I thought throughout the day she was really brave in coming for a lot of cross balls which we knew Celtic were going to do today.
“People will say penalties come down to a lottery, but I know how much prep work she’s put in this week along with Chris Flockhart, our goalkeeping coach, in their analysis and being ready for those types of moments.
“I’m really pleased for them because people think those bits of the job are the unsung bits where you don’t get the rewards, but we absolutely got it today.”
Most pleasing of all for Crichton, however, was her side’s never-say-die attitude when behind in the game.
They settled down in the second half after a thrilling five-goal opening period as the Head Coach praised the side’s togetherness.
She added: “We’ve had a fair bit of that this season. We’ve had some tough moments and it’s probably put us in good stead, even at half-time.
“It was a crazy first half and we were still trailing in the game, and you know how important the next goal is in the game.
“I just felt the players, right through every player and even those on the bench that didn’t come on, every staff member, we were all in it together.
“It was always going to be a tough afternoon and it was the type of fixture that you need to win. We knew what was at stake.
“There was so much pressure and chat around the cups and the success we’ve had here, and we don’t want to lose that. We’re just delighted that we’re in a cup final.”
VIP HOSPITALITY: Combining all the passion, excitement and joy of football with an unrivalled choice of suites and packages, a matchday at Ibrox can be exactly what you want it to be
RANGERS STORE: Shop all the latest offers at the Rangers Store in-store or online
TICKETS: Secure your match tickets for women’s first-team games at Ibrox Stadium and Broadwood Stadium