Vilahamn was appointed as Tottenham Women's new head coach shortly after Postecoglou's arrival in and the Swede told talkSPORT in the summer about how he was trying to replicate the Australian's style of play in his new role.
It has certainly had the desired effect as Spurs have been one of the stories of the Women's Super League (WSL) season, winning plaudits for their attractive brand of football.
Despite recent heavy defeats to Manchester City and Manchester United, there is still plenty to be excited about for Spurs - who sit in sixth place in the table - and Bartrip says Vilahamn has given
belief to the squad after an underwhelming season last year.
Speaking exclusively to talkSPORT, Bartrip said: "There are similarities [between Vilahamn and Postecoglou]. I think you can see very clearly that there are. They want to play a way and they're going to play a way where it doesn't matter who the opposition is.
"We're going to play the Tottenham way and in the next few years, you're going to see it be successful because that's what the club wants.
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"So, in that way, it's actually a really refreshing thing to be a part of [because] you know that this is the way we want to play and you just have to adapt to it. I'm lucky that I think this style suits me a
lot, but at the same time, I think it's really important that as footballers, you have to be adaptable.
"The biggest thing Robert's brought to us is just to be brave and I think that comes on the pitch [and] off the pitch [and] it puts people out of their comfort zone and I don't think a lot of people are used
to it.
"He's given me a lot of confidence. I am a confidence player - I'm not going to shy away from that - and he's believed in all of us I think and it's not easy to be a manager of 26 players.
"He is definitely a manager you want to play for. He's actually a really funny guy, too, and I think it helps when sometimes, you feel like they're a real human and you can talk to them about other
things that doesn't even involve football. To be able to connect in that way is so important."
Bartrip has excelled this season for Spurs and worn the captain's armband in Bethany England's absence, with the Lionesses forward missing most of the season through injury.
The centre-back's performances have impressed her manager, with Vilahamn touting Bartrip for a future England call-up, and representing her country would be a dream come true for the 27-year-old.
Post-match press conference: Ange Postecoglou (Premier League: Tottenham 4-1 Newcastle)
"I'd be lying to say that wasn't a dream of mine. It is [a dream] and I think I've dreamt of it since I was a little kid. But I can only do what's within my control. Right now, Tottenham's in my control," she explained.
"It's all about the team for me. If we could get Champions League, that would be amazing. But at the same time, I think we just need to take every game as it comes. We really do. This league has got
tougher and tougher every single season and teams are beating teams that you don't expect."
Playing for the Lionesses would cap off a remarkable turn-around for Bartrip, who has openly spoken about her struggles with anxiety, depression and anorexia as a teenager.
The 27-year-old now uses her platform to help create change as a mental health advocate and will be a part of the Spurs squad that walks out at the Tottenham Hotspur stadium this weekend as part of a huge North London derby in the WSL against Arsenal.
Spurs have never beaten Arsenal - but did share a thrilling 3-3 draw with their locals in the Conti Cup in midweek - but Bartrip believes this could be the year they get one over the Gunners.
"I really hope so. There's a really good aura around the club at the moment [in both the] men's and women's [teams] and I think that's also a massive thing in [terms of] how you play," she finished.
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"I think you watch the men's [team] and they're doing really well. With us, we've got a new style and a new identity and people want to watch it. Hopefully, we can bring that style and give them a proper game because that's what North London Derbies are about right?!"