Buttler hit an unbeaten 110 as England, chasing Australia's score of 205, recovered from 114-8 to reach 208-9 and secure a 5-0 series whitewash for the first time against the visitors.
Man-of-the-match Buttler was also named player of the series after averaging 137.50 across the five matches.
"Today was mesmerising, with Buttler playing probably at the top of his game," Morgan told Sky Sports News. "His batting with the lower order was exceptional.
"It took all of his experience and everyone in that changing room is very proud of what he did. Jos really did pull something special out to get us over the line. It was outstanding. He's in control - he's a very cool, calculated customer with a lot of ability. In this white-ball team, he is a key part.
"He has come back from the IPL having dominated the back end of the tournament, he has played in tournaments around the world, and he has got back in the Test team which is extremely exciting for us and everyone watching at home."
England face Australia in a Twenty20 match on Wednesday, before facing India in T20 and ODI competitions.