Hughes was appointed Southampton boss on Wednesday following the sacking of Argentine Mauricio Pellegrino and his side, 18th in the Premier League, struggled in the opening 45 minutes on Sunday against League One promotion chasers Wigan.
The Saints, who were last FA Cup champions in 1976, are 11/1 (12.0).
"We are looking exclusively to the end of the season and we want to be a Premier League club and win the FA Cup", he added.
"But the time I've been with them, I've seen good quality and application and maybe they've been hurt by the criticism of themselves, as individuals and as a group".
The 24-year-old has gone from being one of the club's most influential players to a peripheral figure, but Pellegrino's dismissal and Hughes' appointment as Southampton's new manager represents a fresh start.
After 62 minutes, they took the lead that the shift in momentum merited, as Hojbjerg was left unmarked 15 yards out and drilled home directly from a Dusan Tadic corner. Sometimes the players' view is totally insular: it's a bit like they are in their own bubble and you have to understand that.
Wigan's breath-taking energetic first-half performance belied their League One status but their lack of proficiency in attack meant they went into the interval level with their illustrious opponents.
"Second half, I thought the game was quite scrappy, although Southampton certainly grew into the game".
Sofiane Boufal's dipping free-kick after 55 minutes was as close as the visitors had come to threatening before Dunkley allowed Byrne's pass to roll back past him into the Wigan penalty area, where Gabbiadini failed to beat Christian Walton one-on-one.
In the first minute of stoppage-time, Southampton right-back Soares surged into the area before side-footing past Walton.
Gabbiadini burst into the Wigan box 10 minutes later and was brought down by Dan Burn, but the Italian's spot-kick was kept out by an acrobatic save from Walton, who parried the ball around the post.
The Latics were left to rue their missed chances when Southampton came out in the second half with more intensity and urgency.