The Manchester United defender is one of only three specialist centre-backs in Roy Hodgson's squad, prompting concern at the sight of the 26-year-old icing his knee at the national team's training camp in Chantilly.
"There's no injury scare there, it's normal," he told a media conference. "I often ice different parts of my body or jump in an ice bath, so [it was] just [a] normal recovery process to be ready for the next day."
Tottenham's Eric Dier, set to start the tournament in holding midfield, can fill in further back if required and Smalling is adamant there is plenty of cover.
"We've got a couple of other people who can play at centre-back as well, I don't think it's a position that's necessarily a worry," he said.
"We're very well covered in all positions."
According to Smalling, England, who exited the 2014 World Cup in the group stage after defeats to Italy and Uruguay, are taking a positive approach but have not set a benchmark for what they hope to achieve in France.
"We're a confident bunch," he said.
"We're obviously a very young squad. I think it's a case where we don't necessarily set targets. Let's go out there and take on the games as they are. I think there's a fearless factor. Who knows where we can go?"
Pressed on whether or not the Three Lions can finally shine on the big stage, he added: "I hope so. We're all of the mind-set that this is our chance and we want to seize that."