The Queensland Reds flanker was a surprise appointment as the New Zealander's first captain since taking over from Eddie Jones this year, despite playing only five Tests - and none for four years.
He admitted the decision came as a shock.
"Full surprise... Joe didn't give any heads up," said Wright, who is Australia's seventh captain in barely a year after Jones chopped and changed.
"I think I will bring a team-first mindset, that's all I've ever tried to do.
"I've got plenty of leaders to lean on, plenty of experienced guys in this team so I am not going to try and do anything above and beyond."
Australia kick off the Schmidt reign in Sydney on Saturday looking to turn a corner after a horror run under Jones, which culminated in failing to reach the World Cup quarter-finals for the first time last year.
It included a humiliating 40-6 flogging by Wales.
But Warren Gatland's men have lost seven Tests on the trot and have not won in Australia since 1969, a record spanning 11 games.
With the odds favouring the Wallabies, Wright insisted he felt no extra pressure despite knowing he could go down as the first Australian captain to lose to the Welsh at home in 55 years.
"We're not really thinking about that," he said.
"A lot of the focus this week has been around us... we're just focusing on our systems we can play, the connections we can grow this week.
"Wales will throw a lot of things at us, but I think if our systems are strong, if we fight and connect together we will do well.
"Wales are going to be very combative," he added, pointing to the breakdown as pivotal.
"They've got a big forward pack, they like to play that heavy style, especially around the breakdown and I think that's where they are going to put a lot of pressure on us.
"But we have an exciting team, lots of enthusiasm around the debutants. For us to be able to unleash that exciting back line we have, the forwards have to do their job up front."
Schmidt picked two debutants in the starting side - lock Jeremy Williams and centre Josh Flook - and another five on the bench.
