They will need to beat Turkey and hope Wales lose to Italy in the group's other game to secure a top-two finish.
Petkovic and his players have come under intense scrutiny since the Italy defeat, but the head coach has called on Switzerland supporters to get behind the team for Sunday's clash in Baku.
"Against Turkey we have another chance to qualify for the round of 16 and we have to bring all of our values and virtues back to the pitch, in addition to the correct tactical plan, solidarity, joy and respect. Then we can do it," he wrote in an open letter published in Swiss newspaper Schweiz am Wochenende.
"We do not always do what you expect from us. We are people who try to meet these demands, but unfortunately we do not always succeed. And that is why we need the support of all of you before this crucial game.
"Your solidarity, your positivity. We will do everything we can to ensure that we can all be happy together on Sunday evening."
Turkey, meanwhile, have endured a dismal campaign so far, suffering defeats to Italy and Wales in their opening two games.
They cannot finish in the top two and must beat Switzerland to come third in the group.
PLAYERS TO WATCH
Switzerland – Granit Xhaka
Arsenal midfielder Xhaka was criticised by TV pundits in Switzerland for his display in the defeat to Italy.
Despite that, no Switzerland player has made more passes (153), had more touches (172) or made more tackles (five) than the 28-year-old at Euro 2020 so far.
If they are going to get the win they need against Turkey, Xhaka will need to be at his best.
Turkey – Burak Yilmaz
Yilmaz enjoyed a stellar season with Lille as they swept to Ligue 1 glory but he has not got going at this tournament yet.
He was involved in 50 per cent of Turkey’s 18 shots against Wales last time out (six shots, three chances created), although just one of those attempts was on target.
This could be the last major tournament for the 35-year-old and he will be desperate to make his mark against the Swiss.
KEY OPTA FACTS
- This will be the second meeting between Switzerland and Turkey at a major tournament. Their first encounter was in the group phase of Euro 2008 where Switzerland, as co-hosts, lost 2-1 to Turkey.
- The last five games between Switzerland and Turkey have produced 17 goals, an average of 3.4 per game.
- Switzerland (D1 L1) are looking to avoid remaining winless in all three of their group stage games at a major tournament for the first time since Euro 2004.
- Turkey have lost both of their games at Euro 2020, by an aggregate score of 0-5. In a full tournament, only Denmark in 2000 (eight) have conceded more goals without reply.
- Switzerland's loss against Italy was their first defeat in all competitions in 2021. The Swiss last lost consecutive matches in October 2020 (vs Croatia and Spain).