Asked how he would rate the season out of 10, the colourful manager said: "Nine-and-a-half out of 10 - we were missing that extra half point."
Simeone, 44, Argentina's most capped player, said he was disappointed but not sad.
"It's a bitter feeling not to reach your target. I'm disappointed but I'm calm. Once you have given your all you cannot do more."
He said Real had raised their game in the second half after Atletico went ahead through Diego Godin in the 36th minute.
"They kept us pinned in our own half and we couldn't move," he added.
"We are told that winning is the most important thing but the support you have from people showed me that there's more to football and it's pointless to cry over this match.
"When you've played as well as you have, you should keep your head up and be proud."
PASSIONATE SIMEONE
Simeone, who spent the match running along the touchline, gesticulating as though he could feel every shot, pass and tackle on the pitch, said defeat would only improve his team.
"You can lose but you can use it as an opportunity to grow further and to continue to compete because Atletico is here to compete," he said.
Atletico, accustomed to living in Real's shadow, have yet to win Europe's most prestigious trophy but their first domestic league triumph after 18 years and a Champions League final have added a new dimension to Spanish and European competition.
"It's a life lesson. You win, you lose, you have to keep going," he said, adding that the supporters should be proud.
"They shouldn't waste any time crying over the season. Yes, they will be disappointed but later they should be concentrating on next season."
Simeone added that he took full responsibility for playing striker Diego Costa, who had pulled a hamstring during Atletico's title-winning game against Barcelona last week.
The Brazil-born Spaniard had to come off after nine minutes.
"I obviously made a mistake," he said. "He wasn't as well as the day before."
(Reporting by Clare Lovell; Editing by Ken Ferris)
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