Messi missed a spotkick in their 1-1 draw at Copa opponents Valencia this week.
"Messi was a born winner," Thiago told a news conference. "Yesterday, he was brave enough to take the ball and take the responsibility for the penalty.
"He did not score, but that is not a problem. We have the best player in the world amongst us, but we do not depend on him.
"We have to exploit and use the power of each player, and if we have players like him or Xavi, we can certainly draw inspiration from them.
"I am only talking about two of them, but there are so many. We certainly are not dependent on Messi."