The Toffees' hopes of reaching the round of 32 are already over, having lost three and drawn one of their first four matches to leave them bottom of the Group E standings.
Unsworth hopes that an experienced starting lineup will help maintain his side's mini revival, though, which has seen them pick up four points from games against Watford and Crystal Palace either side of the international break.
"We are going to pick a team to win, and we will pick a strong team and one we feel is the right team," he told reporters. "We will be respectful to our fans because whoever turns up with our fans tomorrow, we put on the Everton shirt and be fully respectful of that so we will pick a team to win.
"We need to perform and we need to win. You've got to have those foundations and those building blocks and I think we have had that and got better each game. We have won a game and drawn a game and this is another game tomorrow night that we want to win. We represent Everton and every time you pull on that famous Blue shirt we have a responsibility to do that.
"It's about keeping that [run] going. That's one thing we spoke to the players about this morning. We want to win the game and we go into the game preparing exactly the same. For me, it is not any different to a Premier League game, a cup game, it doesn't matter. It is a game that we represent Everton and that is really important that we put on a performance and try to win."
Atalanta, unbeaten in Europe so far this season, require a point to book their place in the knockout phase.