The Blues were comfortably beaten by Atalanta on Thursday night and now have to travel to take on the Saints in the Premier League.
Speaking to the media ahead of Sunday’s game, Unsworth said: “I think we always owe it to the Everton fans to perform. Our players know that. They know my feelings and sentiments towards the great Everton fans.
“I think they do owe them a performance and I think, and know, they owe them a win.”
Unsworth wants to put Thursday night in the rear view and move on quickly.
It was a point he reiterated on Friday afternoon.
He said: “We’ve got to put it to bed very quickly. The players know exactly how I feel. They know I feel they let the club down.
“The manner of the performance was unacceptable.”
Domestically, Unsworth has somewhat righted an Everton ship that looked to be sinking at a rapid pace.
Unsworth is looking to build on those two most recent results come Sunday lunchtime.
“That’s one thing we’ve tried to do since I’ve got the job, build confidence and performances. Coming back at Watford was fantastic, coming back at Palace showed the players have desire and fight,” the 44-year-old said.
“Hopefully we will show that fight and desire to win a game and move us into the middle of the table. That will settle us down.”
Oumar Niasse banned
Unsworth’s side will be without Oumar Niasse on Sunday afternoon, as the striker begins his two-game suspension after being found guilty of simulation during the trip to Crystal Palace.
It means Everton will have to call on either Dominic Calvert-Lewin or Sandro Ramirez to fill the place of the in-form striker that was once without a Finch Farm locker.
Offering up his opinion on the suspension, the former Everton defender said: “We will have to accept the decision. There is no appeal, but it doesn’t mean to say we agree with it.”
He continued: “I know Oumar. He will always take an opportunity to have a shot on goal. Having seen the replay 50 times, myself, there is contact. How much contact is allowed? That is open to debate.
"When we find that the referee after the game has reviewed the game and continues to state it is a penalty, that is where there is a problem.”
The Blues have settled on a three-man shortlist after five weeks of searching but it is unlikely Unsworth’s name is one of the three.
When quizzed on whether or not he knew his future, the interim boss commented: “If we are further down the line to getting a permanent manager, that’s fantastic.
“There was never any guarantees. I have spoken to the board on a daily basis, we have taken it game by game and given it everything. The players have been focused on the next game. The sooner it’s sorted the better. I think that’s a fair comment.”