A 1-0 home loss to Manchester United on Saturday has left Chelsea sixth in the standings on 48 points with five matches remaining. With several teams closing in behind them, their hopes of qualifying for next season's Champions League have been severely dented.
Chelsea's problems have been compounded by their struggles in front of goal. They have failed to score in their last four league defeats, matching their longest such drought since 1912.
They next travel to ninth-placed Brighton & Hove Albion on Tuesday.
When asked whether he feels the owners still believe in him, Rosenior was emphatic.
"100%," he told reporters. "They have been supportive of me, and our daily conversations have been supportive.
"We know we want to win games of football now, but that doesn't go against the fact that we want success and consistent success in the long term."
Rosenior was confirmed as Chelsea's new head coach in January on a contract running until 2032, following the departure of Italian Enzo Maresca on New Year's Day.
The 41-year-old Englishman is the West London club's fourth permanent manager appointed since Todd Boehly's takeover in 2022.
"We have to win," Rosenior said. "That is what this club demands, and rightfully so, and that is what the fans expect. It is about winning football - that is what football is about.
"You can't speak about the long term if you aren't doing the job in the short term. Being really respectfully honest, we haven't done well in recent games, and that is on my shoulders as the head coach of the team."
On the injury front, Estevao will miss the trip to Brighton, while fellow forward Joao Pedro will be a late call.
"Joao has been on the pitch today. We will make a decision on him tomorrow morning," Rosenior added. "Estevao is definitely out for tomorrow, and we are doing extra tests on him."