Messi, 27, won the Golden Ball after scoring four goals in Brazil, but was subdued in Sunday's final in Rio.
Sabella said Messi's award was "very deserved", adding: "He played a great World Cup to get us where he did."
Messi said of the award: "The truth is it doesn't interest me at this moment.
"We wanted to win the World Cup for all the people in Argentina and we couldn't do it.
"We tried, but we didn't have the luck we had in other games."
All of Messi's goals at the 2014 Fifa World Cup came during the group stage, with a double against Nigeria following goals against Bosnia-Hercegovina and Iran.
But the four-time world player of the year failed to score in the knockout stages, and he and Gonzalo Higuain were guilty of being wasteful in Sunday's final.
"I'm not sure we saw the best of Messi," said Match Of The Day presenter Lineker. "In the final he was largely suppressed."
Former England defender Rio Ferdinand added: "Messi did some fantastic things but he wasn't doing it consistently."
But Sabella said Messi was "a fundamental factor for where we ended up".
The 59-year-old added he was proud of his players, and admitted they had paid the price for missing chances.
Mario Gotze scored the only goal in Rio, volleying home with seven minutes of extra time remaining.
"Beyond the pain of the defeat in the final they can look themselves in the eyes and say they gave everything for Argentina," Sabella said.
The former Leeds and Sheffield United player refused to discuss his future amid reports he was preparing to stand down.
He said: "I cannot speak about the future, the future for me now is to be with the players and my people - the coaches and my family - and to rest a bit."
Midfielder Javier Mascherano said: "The pain is immense. We wanted to win this for the people of Argentina, for those who came here to support us, but we lost.
"We have represented our country the best we could.
"We have to lift our heads despite the pain. We gave everything we could out there."