Poland, who beat Switzerland on penalties on Saturday, had not won a game before the clash with Croatia, registering three successive draws in the group stage.
"Saturday's game was important for me as I played my first game in such a big competition," Fonte said. "If the coach considers it, I am ready to play the next game."
Portugal beat a Croatia team flying high after their 2-1 come-from-behind win over holders Spain in their final group game.
Fonte believes everyone in the Portugal squad feels valued.
"All the players feel important," said Fonte, who made 32 Premier League appearances for Southampton last season.
"That is what the coach makes us believe. I am ready to start just like the other 22 players in the group. We work daily and the coach tells us that he believes in all of us. That gives us hope and makes everyone work at their best."
Portugal reached the semi-finals of the competition four years ago before losing to Spain on penalties.
"We know very well what our philosophy is," Fonte said. "The important thing is to recover and be as fresh as possible.
"I know that whoever plays will give its all and whoever is on the bench will be ready."
Portugal returned to practice on Monday after a day off. Joao Moutinho trained separately from the group while Raphael Guerrero and Andre Gomes were limited to doing specific exercises in the gym.
Guerrero and Gomes both started against Croatia and Moutinho was on the bench.
(Reporting by Adriana Garcia, editing by Ed Osmond)
