Paolo Guerrero scored the only goal of the game with just over 20 minutes to play to consign Rafael Benitez's side to defeat.
Chelsea had overcome Monterrey in the semifinals to face the Copa Libertadores holders and Mata has admitted that he felt optimistic about their chances during the match.
"It couldn't be done," Mata wrote on his Grada 360 blog. "The dream of becoming the club world champions vanished with the final whistle.
He added, "I had a feeling that we were close to clinching the trophy; that we created enough chances to, at least, score; that, although our performance was not brilliant, we were competitive until the very end.
"In fact, it was their goalkeeper, Cassio, who was awarded man of the match thanks to those saves I'm talking about. We knew that Corinthians was a great team: a very physical and competitive side."
Chelsea will now return to England to attempt to revive its fading challenge for the Premier League title.
The European champions raced into top spot in the early weeks of the new campaign but a disappointing run of form led to the sacking of Roberto Di Matteo and a drop to third place.
"It's a tough moment, especially for the Chelsea fans that came to Japan and those who were supporting us from home," Mata continued. "Thank you so much to all of you for your unconditional support.
"I hope we can enjoy good moments and lift more trophies for the club and for you very soon. We're still playing to win four trophies and we will give everything we have to success in each of them."