Liverpool slumped to a 2-0 defeat at Napoli on Tuesday in the UEFA Champions League.
Chelsea were also beaten in their opening match after losing 1-0 to Valencia at Stamford Bridge.
Borussia Dortmund and Barcelona could not be separated during a goalless draw in Germany.
Elsewhere, Ajax won 3-0 against Lille on the opening matchday, Red Bull Salzburg scored six to top Genk and Inter Milan drew 1-1 with Slavia Prague at the San Siro.
Tuesday's Champions League Results
Red Bull Salzburg 6-2 Gent (Group E)
Napoli 2-0 Liverpool (Group E)
Inter Milan 1-1 Slavia Prague (Group F)
Borussia Dortmund 0-0 Barcelona (Group F)
Benfica 1-2 RB Leipzig (Group G)
Lyon 1-1 Zenit Saint Petersburg (Group G)
Ajax 3-0 Lille (Group H)
Chelsea 0-1 Valencia (Group H)
Group E (Played, Won, Drawn, Lost, Goal Difference, Points)
1. Salzburg: 1, 1, 0, 0, 4, 3
2. Napoli: 1, 1, 0, 0, 2, 3
3. Liverpool: 1, 0, 0, 1, -2, 0
4. Genk: 1, 0, 0, 1, -4, 0
1. Slavia Prague: 1, 0, 1, 0, 0, 1
2. Inter: 1, 0, 1, 0, 0, 1
3. Barca: 1, 0, 1, 0, 0, 1
4. BVB: 1, 0, 1, 0, 0, 1
1. Leipzig: 1, 1, 0, 0, 1, 3
2. Zenit: 1, 0, 1, 0, 0, 1
3. Lyon: 1, 0, 1, 0, 0, 1
4. Benfica: 1, 0, 0, 1, -1, 0
1. Ajax: 1, 1, 0, 0, 3, 3
2. Valencia: 1, 1, 0, 0, 1, 3
3. Chelsea: 1, 0, 0, 1, -1, 0
4. Lille: 1, 0, 0, 1, -3, 0
Liverpool failed to produce their best in Italy after a frustrating night in Naples. A tepid first half saw the champions on the back foot, but Napoli could not fashion an opener.
The Reds worked their way into the game in the second half, but the hosts continued to be the aggressors as they chased a goal.
With the Premier League team in the ascendancy and chasing victory, it was Napoli who finally broke the deadlock during their quietest part of the match.
The referee gave a penalty after Andrew Robertson fouled Jose Callejon, and despite the forward appearing to dive, the video assistant referee did not overturn the call.
Dries Mertens scored from the penalty, and Fernando Llorente made it 2-0 in stoppage time to wrap up the win.
Jurgen Klopp defended his team's performance after the final whistle, per beIN Sports:
It was a bad night for Chelsea at the Bridge after Ross Barkley missed a late penalty to spurn the chance of a point.
The Blues lost Mason Mount to injury in the first half, and the hosts struggled to create chances after the youngster's substitution.
Valencia created little opportunity, but poor marking from a free-kick allowed Rodrigo to flick home the opener after 74 minutes.
Chelsea nearly earned a reprieve with five minutes left on the clock. Daniel Wass was adjudged to have handled the ball in the box by VAR, and Barkley stepped up to take the spot-kick. The England international debated with his team-mates, claiming the ball to take the penalty, and the former Everton player hit the bar.
BVB were denied the chance of an opening win against Barca after Marc-Andre ter Stegen saved Marco Reus' second-half penalty.
England winger Jadon Sancho was tripped by Nelson Semedo in the box after 57 minutes, but Reus could only watch as Ter Stegen kept out his effort.
Lionel Messi made his first appearance of the season, rising from the Catalan bench as a substitute after completing his recovery from an ankle injury, but the icon's presence wasn't enough to inspire his team against the Bundesliga side who had the better chances to win the game.
Erling Braut Haaland's first-half hat-trick in his Champions League debut helped Salzburg crush Genk 6-2 as manager Jesse Marsch became the first American to coach in the UCL. New additions Quincy Promes and Edson Alvarez both scored for Ajax at home to lift last season's semi-finalists to a 3-0 win over Ligue 1's Lille.