The Reds were back in lower-level competition for the first time since Klopp's first season at Anfield, when they lost to Sevilla 3-1 in the 2016 Champions League final in Basel.
On Thursday, Liverpool celebrated its return to the Europa League by defeating Austrian club LASK 3-1 after coming from behind once more.
After receiving a low cross from Ryan Gravenberch in the middle of the pitch, Luis Dáz made a precise finish into the top of the net to give the visitors the lead in the 63rd minute.
In the 88th minute, Mohamed Salah scored after coming off the bench to complete the comeback.
In the 14th minute, Florian Flecker scored the opening goal against three-time champion Liverpool, beating backup custodian Caoimhin Kelleher from a corner kick.
Darwin Nez's penalty kick goal 11 minutes into the second half, following Philipp Ziereis' foul on D'az, gave the visitors the equaliser.
When Liverpool defeated Wolverhampton 3-1 on Saturday in the English Premier League, manager Jürgen Klopp made 11 changes to his starting lineup.
The Reds were back in lower-level competition for the first time since Klopp's first season at Anfield, when they lost 3-1 to Sevilla in the 2016 final in Basel.
Union Saint-Gilloise and Toulouse tied 1-1 in another Group E match.
The winner of the Europe Conference League, West Ham, had to come from behind to upset Serbian newcomer TSC Baka Topola 3-1 at London Stadium in Group A.
Nemanja Petrovi's own goal in the 66th minute ignited West Ham's comeback. In his first game for the Hammers since signing in the summer, Mohammed Kudus scored the second goal with a header four minutes later, and replacement Tomas Souek added the third with a similar effort.
Three minutes after halftime, the Serbian team's Petar Stani defeated custodian Ukasz Marek Fabiaski one-on-one.
Brighton's first appearance in a European competition was hurt by a 3-2 home loss to AEK Athens in Group B.
Six minutes from the end, substitute Ezequiel Ponce scored the winning goal to give the Greek team a three-goal lead.
Brighton, which is competing in Europe for the first time in the club's 122-year existence after finishing a club-best sixth in the English Premier League last season, forward Joo Pedro converted from the penalty spot in either half.
Pierre-Emerick As the two previous Champions League champions faced off in yet another game in one of the most difficult groups, Aubameyang scored his second goal in the 78th minute to rescue a 3-3 draw for Marseille at Ajax.
Marseille was without its coach Marcelino on Wednesday since he quit after just a few games in charge.
Roma, which finished second last year in Group G, defeated Sheriff 2-1 in Tiraspol thanks to a goal from Romelu Lukaku in the second half. Lukaku scored again after coming from Chelsea.
Earlier, Cristian Tovar tied the score in the second half after replacement midfielder Leandro Paredes scored from a deflected free kick in first-half stoppage time to give the visitors a 1-0 lead.
Jose Mourinho's Roma is attempting to make it to its third consecutive European championship game.
Also in Group G, Slavia Prague defeated Servette 2-0 to earn three points for Geneva.
Atalanta defeated Raków Czestochowa 2-0 in Group D with to goals from attacker Charles De Ketelaere and substitute Éderson, while Rangers defeated Real Betis 1-0 in Group C.
In the second minute, Ludovic Blas scored the competition's first goal of the year to help Rennes defeat Maccabi Haifa 3-0 in Group F. Villarreal, the 2021 Europa League champion, was defeated by Panathinaikos 2-0 in the other matchup in the group.
Leverkusen defeated Sweden's newcomer Häcken 4-0 in Group H thanks to goals from Florian Wirtz, Aminde Adli, Victor Boniface, and substitute Jonas Hofmann.
CONFERENCE LEAGUE OF EUROPE
Legia defeated Aston Villa 3-2 in Warsaw, with the Albanian forward Ernest Muçi scoring twice in the second half to prevent the English team from reaching the group stage of a competition for the first time since the 2008–09 campaign.
In the Group E match, Villa, the 1982 European Cup champions, had to come back twice after falling down.
Just three minutes after Pawel Wszolek gave the hosts the lead in the third minute, Villa attacker Jhon Duran headed in the equaliser. With his first, Muçi made it 2-1 in the 26th minute, and later, defender Lucas Digne made it 2-2.
With a 4-3 victory over Alkmaar in the other group's match, Zrinjski made his triumphant debut for a Bosnian team in Europe.
The runner-up from the previous year in Group F, Fiorentina, began their season with a 2-2 draw at Genk in Belgium. Defender Luca Ranieri scored both of Italy's goals with two consecutive headers.
K Klaksvk, the first Faeroe Islands team to advance to the group stage of a championship in Europe, suffered a 2-1 defeat at Slovan Bratislava.
In Group B, the host Maccabi Tel-Aviv team triumphed 3-2 over the Icelandic team Breidablik.
Eintracht Frankfurt defeated Aberdeen 2-1 in the group's opening match.
