Marsh also posed for a picture with his brother Mitchell - who scored a fantastic 181 in Perth - and their father Geoff who was an opening batsman for Australia from 1985 until 1992.
"Captaining an Ashes-winning side, it's an amazing feeling," Smith said after Australia bowled England out for 218.
"So much preparation has gone into this Ashes series. The way we've gone about it has been spectacular.
"So many different emotions are coming out right now, I'm that excited.
"I'm just so proud of the boys. The way we've been able to win this series and wrap things up here in Perth and get that urn back, it's been quite amazing.
Read more: The gulf between Australia and England
"The (bowlers) have done a terrific job to get us the 20 wickets that we've needed in every game.
"We haven't won a toss and we've probably had the toughest of the conditions as well. I'm just really proud of everyone in that dressing room."
Josh Hazlewood grabbed a five-wicket haul in the second innings, with fellow seamer Pat Cummins cleaning up the tail as Australia's pacemen continued their dominance in the series.
Read more: Australia reclaim Ashes with emphatic win over England
"The bowlers have done a terrific job throughout the whole series ... I thought Josh Hazlewood was magnificent today to get five wickets," added Smith, who also praised Mitchell Marsh for forging a 301-run first-innings partnership alongside him for Australia's fifth wicket.
"That really set the game up for us, to get us in the lead.
"We're going to celebrate this one first. The Boxing Day Test match is an amazing occasion, hopefully we can get ourselves 4-0 and maybe 5-0 in Sydney. Everyone has been fantastic to get us the result we deserve."
England captain Joe Root was downcast after emulating his predecessor Alastair Cook in surrendering the urn with two games to spare.
"Yeah, it is very difficult to take," he said. "They've outplayed us in all three games. We've got to be better.
"We've got to make sure we go to Melbourne and prepare well and put in really good performances there."