The Argentina forward and four-times World Player of the Year barely threatened the Atletico Madrid goal at the Calderon as Barca fell behind to Koke's fifth-minute volley and were unable to turn around the 2-1 aggregate scoreline.
Messi has so often shone on the biggest stage in club soccer but was again superbly marshalled by the Atletico Madrid players and has not scored a goal against the Madrid club in their last six meetings in all competitions.
Barca coach Gerardo Martino appeared to deploy his compatriot on the right of a three-man attack, away from his usual central position, with Cesc Fabregas roving in the middle and Neymar mainly on the left.
Messi skewed a shot high and wide in the third minute, missed with a header in the 13th and sent a low effort past the post in the 24th from Neymar's cross but faded out of the rest of the game and was unable to rescue Barca in the way he has done so many times before.
It was a strangely subdued performance and Spanish media reported the normally electric Messi had run only 6.8 kilometres during the game, only 1.5 kms more than Barca goalkeeper Jose Manuel Pinto.
"We wanted Messi to be in a position to take on defenders in a one-on-one from the right wing," Martino, who comes from Messi's home town of Rosario, told a news conference.
"He did not feature much in the game but he did have those two chances with the header and after great play from Neymar."
Barca's elimination means they failed in their bid for a record-extending seventh consecutive appearance in the last four of Europe's elite club competition.
However, after beating Atletico Madrid to claim the season-opening Spanish Super Cup, they still have a chance of two more titles this term.
They are a point behind Atletico Madrid in La Liga with six games left and play arch rivals Real Madrid in next Wednesday's King's Cup final in Valencia.
Martino conceded that Atletico Madrid had deserved to go through on Wednesday.
"In reality, the moments when we couldn't do what we had planned, what Barcelona normally does, are to do with the virtues of our opponent," he said.
"Their intensity, the way they defend, the number of players closing ranks near their penalty area.
"At times it is hard to find the depth. We tried in any way we could, including by making some changes, but obviously we couldn't do it."