The Catalan giants wasted the opportunity to take a valuable lead in the Copa del Rey semi-finals against Valencia as Messi missed a penalty in the second half of the match, which ended 1-1.
"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."
Despite defeating Real Madrid earlier in the Copa del Rey, Barca are seven points adrift of Los Blancos in La Liga, but Thiago has refused to admit defeat.
"This team has shown a lot of things in the last seasons, of course we can turn things around," he noted.
"We need to go little by little and prepare for one match at a time."
The 20-year-old attacker then admitted that Barca were lucky that the referee of Wednesday's match failed to see Jose Manuel Pinto handling the ball outside the area, which would have earned the goalkeeper a red card.
"Referees have always existed in football, sometimes they make correct decisions and sometimes they do not," Thiago added.
"Luckily, he did not make a correct decision yesterday. I am not one to judge.
"We want to play a match which is good and has 22 players on the field, referees should not be talked about."
Starting in November and continuing through to the middle of February, Goal.com is publishing exclusive extracts from Graham Hunter's highly-anticipated new book, 'Barca: The Making of the Greatest Team in the World'. Friday's extract looked at how Barca suffered rare disappointment at the hands of Real Madrid in a gripping finale to last season's Copa del Rey. Don't miss it!