"Absolute boss in Europe" read the Ta Nea newspaper headline. "This team has a past, a present and a brilliant future that will force the team to add more stars on their strips."
The Greeks beat the 2006 European champions 93-91 in a thrilling final on Sunday, despite a fierce counter attack by the Russians halfway through the game.
They have won all four of their European titles in 11 years, three of which were under current coach Zelimir Obradovic who took over in 1999.
Thousands of fans poured into a central Athens square, honking their car horns, lighting flares and chanting the team's anthem until early in the morning.
"Lord of the Rings" said the daily Eleftherotypia, adding the team's deep bench and options with which Panathinaikos can play made it hard for any European team to beat them.
Six of their players scored double digit-points compared to CSKA's four, as Panathinaikos showed versatility in attack.
CSKA's Greek guard Theodoros Papaloukas, who almost single-handedly tried to keep his team in the game in the third quarter ignoring fans' jeers, had 23 points but was reduced to tears after the final whistle.
"Every year is better than the last and we hope we also succeed next year in Madrid," club president Pavlos Giannakopoulos said.
Panathinaikos have already won the domestic cup and are expected to easily win the championship with play-offs due to start later this week.
"This is the emperor of Europe," said the daily Eleftheros Typos said.