Vilahamn was appointed in July from his native Sweden after leading BK Hacken to consecutive Swedish Cup finals. He takes charge of a Spurs side who narrowly avoided relegation last season, finishing ninth in the 12-team Women's Super League.
However, he said he is determined to get the team playing a more attacking, free-flowing style of football and that his ambition is aligned with that of Postecoglou, who has started his reign at the men's team with four impressive wins in six Premier League games.
"We shouldn't expect Tottenham to win the league this year, (but) we need to make sure we show the supporters, the board members and everyone that we play better football," Vilahamn told reporters.
"We have an identity that looks like Tottenham. Tottenham want to play a style with the men's team and the women's team, academy and I think me and Ange try to do the same stuff with how to play.
"Not the same formation all the time but trying to be brave enough to play good, offensive football and in the long run, win games."
Spurs, who begin their WSL season with a trip to face holders Chelsea at Stamford Bridge on Sunday, were promoted in 2019 and finished fifth in the 2021-22 campaign but have never produced the dynamic football of some of their rivals.
Despite not being able to compete with the lure of the traditional WSL powerhouses, Vilahamn was determined to develop young players as well as adding vital experience in the likes of Finnish midfielder Olga Ahtinen (26), Swiss defender Luana Buhler (27) and Czech goalkeeper Barbora Votikova (27).
However, a tilt for the top three and qualification for the Champions League would be too much to ask for this season.
"I think a good step the first year would be to try to reach the top six of the table and try to show results and performance," said Vilahamn, who began his coaching career in 2008 at men's side Ytterby IS and helped them to back-to-back promotions.
The signing of Scotland forward Martha Thomas from Manchester United will help take the pressure off last season's top scorer Beth England, who is missing for the first few weeks of the campaign as she recovers from hip surgery.
But it's off the field where more appointments have been made with Vilahamn keen to make improvements in every aspect.
"I think from the inside we have gained a lot more staff now, we have nutrition, more people in the gym and more people working," defender Asmita Ale said.
"We have spreadsheets about our sweat and stuff from training. I think Robert likes that insight... we also had a lady come out to look at our eyes for vision testing. We are just trying to get all the one percents to be better."