"He has all the ingredients necessary to win the world championship but he has to be in a competitive car," said Dennis.
"One race is one race. We will see how four races go.
"But I don't have any concerns about his temperament, his focus or his commitment. And he is prepared to make whatever sacrifices are necessary - that is very clear.
"He has a phenomenal mentor in Jenson, they get on very well. He will keep Jenson honest."
Dennis said the Dane's performance also justified his promotion to the team at the expense of Sergio Perez.
"I don't think he could have done a better job," Dennis said of Magnussen.
"He made no mistakes at all throughout the weekend. He never put a wheel off the track, followed all the instructions but pushed very hard at the right times.
"I have nothing but praise for him. Third place [on the road] in your first grand prix, with the complexity of the regulations [and] a challenging qualifying in both wet and dry conditions - who could ask for more?
"It justified the selection process.
"Giving him the opportunity, [it] is always difficult to take those decisions as you can be wrong, and I am pleased that this one was right."
Below is a list of all drivers who have finished on the podium on their Grand Prix debut.
Kevin Magnussen is number 17, the first since Lewis Hamilton managed it at Melbourne, for McLaren, back in 2007.
Giuseppe Farina 1st Britain 1950
Luigi Fagioli 2nd Britain 1950
Reg Parnell 3rd Britain 1950
Alberto Ascari 2nd Monaco 1950
Dorino Serafini 2nd Italy 1950*
Peter Whitehead 3rd France 1950
Jean Behra 3rd Switzerland 1952
Karl Kling 2nd France 1954
Masten Gregory 3rd Monaco 1957
Giancarlo Baghetti 1st France 1961
Peter Arundell 3rd Monaco 1964
Mike Parkes 2nd France 1966
Reine Wisell 3rd USA 1970
Mark Donohue 3rd Canada 1971
Jacques Villeneuve 2nd Australia 1996
Lewis Hamilton 3rd Australia 2007
Kevin Magnussen 2nd Australia 2014
*Shared drive with Ascari