Fernando Santos' men were dominant for long periods against Austria but were left to rue Cristiano Ronaldo missing a second-half penalty in the 0-0 draw at Parc des Princes.
Portugal are now two points behind leaders Hungary after also sharing the spoils in a 1-1 stalemate with Iceland in their opening game.
And Carvalho admits doubts are starting to creep into the Portugal camp but has urged his team-mates to improve ahead of their must-win encounter against group-leaders Hungary.
"We have to get better," he said. "I believe we played better than in the first game. We are going to grow, we will grow and it's important to win.
"We are going to keep going as a team, as we did today - and we have to win.
"We wanted to win. We did more than enough to win the match and we didn't win, so that's why we are a little bit more worried - because looking at the match we played, we deserved to win it. Now we are going to think about that match [against Hungary]."
Victory in Lyon on Tuesday would guarantee a place in the knockout stages for Santos' charges but Carvalho refused to look too far ahead.
"In order to win [Euro 2016], the team needs to grow," he said. "And to grow, it's necessary to win games.
"That's what is missing. If we had done, morale would be higher and confidence would be greater. But after the match we played, I don't think we need to be so worried.
"We have to be prepared to win. We depend on ourselves and that’s important."
"I don't know [if I will return to Portugal]," he added. "In my head is representing my country and I'm not concerned about that [at the moment].
"I think the time to return to Portugal already passed because I'm 38! Even though I feel really good. But in football you never know.
"I still don't know. It depends on the offers I will have. After the Euros I will meet with the people at Monaco. They have been in touch, I don't know what they wanted to say. But in terms of playing, I will be available."