The Spanish champions, who had two goals ruled out in the second half after VAR reviews, dominated the match and were leading 2-1 with 10 minutes left thanks to goals from Messi and Antoine Griezmann.
But it was Atletico who booked their place in Sunday's final against Real Madrid, levelling thanks to a penalty from Alvaro Morata before Angel Correa struck the winner after Griezmann gave away possession.
"We need to try and continue playing as well as we did today for the rest of the year but make sure we don't make the childish errors we made today," Messi told reporters.
"We controlled the game for around 80 minutes, we played at a high pace, we attacked all the time and created lots of chances. But in the last 10 minutes we made big and we let a game slip which we had under control."
The defeat continued a poor start to the new year by the league leaders, who were held to a 2-2 draw at struggling Espanyol last week which left them level on points with second-placed Real.
That result led to further criticism of coach Ernesto Valverde, although Messi said the team backed their manager.
"We still have confidence in him and we will work hard so we can improve, but it's normal that there is discontent when there's a defeat and people feel the team is not playing as they would like," Messi added.
"We have to be more united than ever, be a strong group and move forward. We are top of La Liga but we have not been playing well recently so we are going to try and recover our best play so we can stay at the top."