Wednesday's 2-0 victory completed a trophy treble for Barca who also won the Primera Liga crown and the Copa del Rey in what has been a remarkable campaign under former club star Josep Guardiola in his first season as coach.
Eto'o's early strike put the Spanish team in front and Messi's header doubled their advantage in the second half, leaving him as the Champions League's top scorer with nine goals.
''I think it will take us a long time to realise what we have achieved today,'' Messi said. ''To score in a Champions League final against Manchester United and win the league title is just unbelievable. It's a dream. This has been an unbelievable season.''
Manchester United were the holders and they had gone into the match at the Stadio Olimpico on the back of a 25-match unbeaten run in the competition, but after enjoying a strong start Eto'o scored in the 10th minute and stole the momentum for Barcelona.
''What we have done is historic, this is fantastic,'' Eto'o said. ''I'm not sure that my goal was crucial for us to win the Champions League but it was certainly important.
''The whole team played fantastic, from Xavi to Iniesta, who was coming back from injury. It's been a great team effort from the start of the season.''
Messi finished second in the FIFA World Player of the Year voting to United's Portugal international Cristiano Ronaldo, however on the night Ronaldo was nowhere near as influential as the Argentine.
There was a lot of media hype about the Ronaldo vs Messi showdown in Rome but Ronaldo said: ''There was no duel. Barcelona were better on the night.''
The United man said that Eto'o's strike had been the most important. ''The first goal really hurt us,'' he said. ''We didn't react. We weren't able to play our game and Barcelona dominated.''
There has been constant speculation about Ronaldo's future with Real Madrid having not hidden their desire to sign the player one day.
Ronaldo wouldn't be drawn on his future, however, when asked about Real Madrid and if this was his last match for Manchester United. ''I don't want to talk about my future right now,'' he said.