"We've set the bar higher in terms of the qualities we will need to show in the games ahead of us so it's not going to be easy," Hughes, who replaced the sacked Mauricio Pellegrino last month, told British media.
"We've given ourselves an opportunity and a chance to turn this around. Results change everything. They change perception, they change people's mentality, they change fans' mentality, it's not all negative now."
Dusan Tadic, who scored both the goals against Bournemouth, has urged the club to keep Hughes beyond the end of the season.
"I think he needs to stay in Southampton because he is a great coach and he's a coach for Southampton – everyone can see that," Tadic said.
"The most important thing now is that we stay in the league but he's great for Southampton."
Southampton next face a trip to eighth-placed Everton on Saturday.
(Reporting by Hardik Vyas in Bengaluru; editing by Amlan Chakraborty)
