Gareth Southgate's men have taken four points from their opening two games against Serbia and Denmark but have failed to hit the heights expected from one of the pre-tournament favourites.
England were second best for long spells of Thursday's 1-1 draw against the Danes and also struggled during the second half of a 1-0 win over Serbia.
However, they have previously bounced back under Southgate from disappointing second games in the group stages of major tournaments.
Three years ago, England reached the final of Euro 2020 after drawing 0-0 with Scotland at Wembley and they were also held to a goalless draw by the United States at the 2022 World Cup before progressing to the quarter-finals.
England only need a draw in their final match in Group C against Slovenia to be guaranteed of progress. Victory will ensure they win the section.
"It's the same position as before (at the last two tournaments). There are calm minds around the camp from players that have been here," Bowen told reporters on Saturday. "We're calm and ready for the challenge on Tuesday."
Southgate accepted England must improve and suggested his side are struggling physically to press as they would like at the end of a gruelling club season for many of his players.
Bowen has been introduced as a substitute in both the opening games and insisted he still feels fresh to make an impact after 50 games for club and country this season.
The 27-year-old believes England are a victim of their own success under Southgate having reached a final, semi-final and quarter-final in the last three tournaments.
But Bowen, a relative newcomer to the England squad, said the mood inside the camp is still positive.
"The mood is really high. We try not to get involved in the outside world because what we've got is a really tight group, a real togetherness," he added.
"We're sat here with four points and it is probably the standards that we've set that it's not two wins (people expect).
"We're still top of the group and we're still in control of our own destiny. We go into Tuesday's game, win that and we're going into the knockouts."
The only absentee from England training on Saturday was Luke Shaw as doubts over the Manchester United defender's chances of playing any part in the tournament grow.
Shaw has not played a minute for club or country since February due to a calf injury and Southgate's decision to bring him as the only natural left-back in a 26-man squad looks increasingly misjudged.
