By SABC Sport
5th June 2024
The Australian's first campaign saw him having to reshape the squad following the summer departure of star striker Harry Kane to Bayern Munich, eventually guiding Spurs to fifth place in the Premier League.
While the team were unable to maintain their early form and eventually fell away from top-four contention, former Celtic boss Postecoglou insists he has "lofty ambitions".
Dawson made over 320 Spurs appearances and was part of the squad which won the 2008 League Cup, although he missed the final against Chelsea at Wembley through injury.
The former centre-back also went on to help Harry Redknapp's side finish fourth in 2010 to qualify for the Champions League for the first time in the club's history.
Dawson, capped four times by England, is confident his old team can continue to move forwards under Postecoglou next season.
"If you look where we were 12 months ago and someone said we were going to finish fifth, just two points behind fourth, then there has certainly been an awful lot of progress," Dawson told the PA news agency.
"The new manager hit the ground running, probably ahead of schedule. I think it was hard for him to come in and get the team playing in the way we are, which is certainly enjoyable to watch.
"Of course there is disappointment we just missed out on the top four, but it is European football for us - and that is certainly a positive."
Dawson added: "I am sure that Ange's aim, and the players' aim, is to try to get some silverware.
"We know everyone wants it - all the fans want it, the owners and the board, that is what they want, but it can be hard.
"But you look at the stadium, at the training centre - fundamentally you just want to keep trying to keep improving.
"So if that can be an improvement in the top four next year with European football â- because Champions League is where our aim has got to be at the start the season, along with other football clubs.
"In another 12 months, what will progress be? Hopefully we can add a trophy and can be in the Champions League â- but there are so many teams striving for the success and you have got to earn the right to do it."
Dawson is a long time supporter of Prostate Cancer UK, regularly wearing the charity's 'Man of Men' badge.
The 40-year-old is joining the 'Cycle On You Spurs' squad on their annual London to Amsterdam 150-mile fundraising ride, and will be taking part in the first leg which starts in Stratford on June 8. The team have raised ã25,000 to date.
"I have a friend who has prostate cancer. It affects one in eight men and it is so sad," Dawson said.
"The guys who have got me involved in this ride, it is a great campaign â- whether my legs will be saying that after it, I don't know, but it is all for a great cause."