Rosler took charge of his first game against Maribor in Slovenia on Thursday but could not stop the Latics' losing run.
The 2-1 loss brought Wigan's first European campaign to an end in the group stage of the Europa League and also made it six defeats in a row.
The first three of those cost Owen Coyle his job, with former Manchester City striker Rosler leaving Brentford to replace him last Saturday.
A hectic first week in the job for the German will conclude on Sunday, and Rosler expects his players to bounce back strongly.
He said: "I don't think it will be difficult to lift them. I think we turn the music on, rock and roll, and we prepare for Sunday.
"They did everything that I asked them to do (against Maribor). Sometimes there are things that we can't control and that's life, so we have to take it on the chin and move on.
"It was a great experience and unfortunately the better team didn't progress."
Rosler's name was sung by the 1,000-strong section of Wigan fans as soon as he emerged from the tunnel at the Stadion Ljudski vrt and, although the result was the same, the reaction was very different.
Former Bolton boss Coyle was very unpopular among supporters, who did not appreciate the move away from the passing style of FA Cup-winning manager Roberto Martinez.
Rosler's philosophy is similar, and he said of his welcome: "This is a big lift. It's always good when you feel you're appreciated by the supporters.
"The supporters have also been fantastic to the players. We did not leave Maribor with our heads down. We got confidence out of that game. We had to do more running than I would have liked but we will recover in time.
"I felt the supporters were happy with what they saw. They saw a team that didn't play as individuals, they played as a team. We had a game plan, the players believed in the game plan, and we pushed for it. That's all we can ask."
The Wigan squad appear to have quickly bought in to what Rosler is trying to achieve, with goalkeeper Scott Carson saying: "We looked a totally different side from the past three or four games.
"I think it was just all down to the energy that we had, everybody was playing as a team.
"Everybody put the effort in and I think it was 100 times better than the effort that we have been putting in lately."
Midfielder Chris McCann, whose controversial sending off badly hurt Wigan's chances against Maribor, added: "In a short space of time we've got confidence already and we're moving the ball really, really quickly, we're creating lots of chances.
"The boys seem like they're playing with a bit of freedom now, they're really enjoying it."
To add further spice to the encounter, the sides sit level on 22 points going into the clash, with Bolton having ended a two-game losing run by beating Doncaster 3-0 last weekend.
Manager Dougie Freedman does not expect the European exit to demoralise Wigan, and he told a press conference: "There won't be any hangover for Wigan.
"Our players are in good spirits and are looking forward to the derby. We've been playing well of late and we need to maintain that. We have got what it takes to go eight and nine games unbeaten."
Freedman, meanwhile, confirmed midfielder Mark Davies is available nearly 10 months after suffering a knee injury.