No revenge for Lippi
Juventus claimed the first trophy of the Italian season with victory via the lottery of penalties after a 1-1 draw with their Serie A rivals in New York.
But Lippi did not believe the spot-kicks success for his troops was retribution for Juventus' defeat to Milan in the Champions League final in the spring.
Lippi merely hopes the triumph in the United States bodes well for the coming months and praised his players for their performance in stifling conditions.
"First, it's necessary to say that all the players have been good due to an incomplete preparation and this hot temperature," said Lippi.
"I think Juventus deserved to win during the 120 minutes because we did something more than Milan.
"This isn't revenge for the Champions League, it's a different thing. This is the first trophy of the 2003/04 season. We hope to continue in this way."
Juve goalkeeper Gianluigi Buffon saved the decisive penalty from Christian Brocchi and lamented the irony of the Super Cup success.
"The paradoxical thing is that I won the Italian Super Cup by stopping one penalty and I lost the Champions League despite stopping two," opined Buffon.
"Anyway, I'm satisfied because we obtained another trophy."
Milan coach Carlo Ancelotti was left to rue a momentary lapse in concentration which cost the European champions victory in the first period of extra-time.
Andrea Pirlo's injury-time penalty appeared to hand Milan the trophy on the Silver Goal rule but Juventus conjured up a last-gasp equaliser from David Trezeguet, with Ancelotti frustrated at the outcome.
Ancelotti said: "In a minute, everything has happened. We scored through Pirlo and then we were inattentive for a few seconds and Juve equalised.
"Both sides have played in a good way, with many sudden counter-attacks. We tried to attack with all the players we had but it went this way."