The Manchester United forward captained England and scored in last weekend's 1-0 friendly win over Romania but he struggled for fitness and form at the end of last season for United, scoring once in their final 10 games.
The 23-year-old faces tough competition for a place in the starting line-up for Sunday's Group D opener against Croatia, with Southgate, blessed with plenty of attacking options in his 26-man squad. "We go there as a squad that's trying to win a tournament," Rashford told British media on Monday. "Whether or not you're starting in the first 11, you've still got a massive role to play if we want to win the tournament.
"Don't get me wrong, everybody wants to be in the first 11 but I think from my experience of being in tournaments you need a squad, you have to have players capable of coming on at different moments and giving that extra spark. "I think in our squad we have that all over the pitch, so to be honest, it (starting against Croatia) is not at the front of my mind."
England, semi-finalists at the 2018 World Cup, face Scotland on June 18 and the Czech Republic four days later after playing Croatia, with all games being held at Wembley.