Victory won the 10th championship - to seal the double - with a commanding 3-0 win over Sydney FC in the grand final and Valeri said the team was well equipped for the challenges that lie ahead.
Valeri inherited the captain's armband after the off-season departure of Australia midfielder Mark Milligan, who now plays in the United Arab Emirates for Baniyas.
Milligan will be replaced by fellow Socceroos midfielder Oliver Bozanic, who has signed a three-year deal with the club after ending his two-year stint with Swiss club Luzern.
Valeri, who has played 52 times for Australia, admitted that wearing the captain's armband did not make him the sole leader of the group.
"Every player here is a leader and it does not really matter who gets the armband," Valeri said.
"It's always a privilege to captain a club like Melbourne Victory, don't get me wrong.
"But there are many leaders in the squad and I'm not talking about just the senior players ... even the younger ones are encouraged to talk and be leaders. Everyone has to stand up.
"This (approach) is passed on from our coach Kevin Muscat who was a captain of this club and he's the leader we all follow.
"We all believe in what we are doing. We are true professionals and we work for each other.
"Mark is gone but I am sure that leadership is not going to be a problem at this club."
Valeri, who returned to Australia at the start of last season to join Victory after 11 years in Italy, said the club was not resting on its laurels.
"We have no illusions about how hard it is going to be to successfully defend our title," Valeri said.
"We expect a stiffer challenge, definitely. But this is what we want ... we want to test ourselves.
"We do not need to say it among ourselves ... we just look at each other.
"Last season is gone and and done and now it's a new challenge.
"We work hard at training because we want to grow and keep getting better.
"We were not satisfied with our performance against Rockdale in the FFA Cup, for example, because we were sluggish in the first half and we could have done a lot better.
"Nobody was happy after the match even though we won and this shows what we want to do and what standards we want to reach."
Victory will host bitter rival Adelaide United in the FFA Cup quarter-finals on 22 September before kicking off its A-League campaign against the same team at Coopers Stadium on Friday 9 October.
