Liverpool endured a frustrating evening at Anfield as they were held to a 1-1 draw by Swiss side FC Sion in Group B.
The pressure on Brendan Rodgers will surely increase as his side now have only two points from their opening two games, in a group they were surely favourites to win when the draw was made.
It started well for the Reds, as Adam Lallana scored his second goal of the competition after good work from Divock Origi on the right-hand side; the Englishman side-footing home after only four minutes.
The Swiss Super Cup winners were level on 18 minutes however, as Xavier Kouassi played a pass over the top of the defence to striker Ebenezer Assifuah, who beat Simon Mignolet from just inside the six-yard box.
The Anfield side could have clinched victory in the last 10 minutes, but Lallana failed to capitalise on a good first touch as his left footed shot was saved by Vanins.
Tottenham earned a valuable point away from home against perhaps their closest rivals in Group J, Monaco, after playing out a 1-1 draw.
Mauricio Pochettino’s side took the lead on 36 minutes, after good work on the right from Nacer Chadli released Dele Alli, who was unable to beat Danijel Subasic from eight yards, only for Eric Lamela to tap in for his second goal in three games.
Leonardo Jardim’s side were almost straight back in it, but winger Alain Traore was unable to beat Hugo Lloris at his near post on 37 minutes.
The second half brought few chances in the opening 25 minutes, but substitute Nabil Dirar managed to evade Danny Rose on the right before whipping in a cross for fellow replacement Stephan El Shaarawy to head in on 72 minutes.
The home side pushed for a winner late on, but a point was probably a fair result after an even game. Spurs move to the top of the group after two games, with four points.
Celtic also have two points from two games after drawing 2-2 with Fenerbahce at Celtic Park, but they really should have taken all three points having been 2-0 up inside 40 minutes.
Leigh Griffiths grabbed his first of the competition on 28 minutes after his initial shot was saved by goalkeeper Fabiano, following Mikael Lustig’s header. Midfielder Kris Commons then added a second four minutes later by converting James Forrest’s cutback.
But the Turkish side were back in it before half-time, as defender Efe Ambrose’s header left Craig Gordon in no man’s land and Brazilian striker Fernandao capitalised. The in-form forward added a second just after the break, as former Manchester United winger Nani’s cross was headed in on 48 minutes.
The result means that Ronny Delia’s men sit second in Group A, but they have thrown away leads in both of their matches to date.
In the other game in Celtic’s group, Molde and Ajax played out a 1-1 draw, as goals from Daniel Berg Hestad and Viktor Fischer respectively means it remains wide open.
In Liverpool’s group, Russian side Rubin Kazan drew 0-0 with Bordeaux, with the main incident in the game being Syarthey Kislyak’s red card on 80 minutes.
Elsewhere, in the other half of Spurs’ group, Qarabag secured a welcome 1-0 victory against Belgian side Anderlecht, as Brazilian Richard scored his second goal in as many games to give the Azerbaijani champions their first points of the campaign.
In Group L, Serbian side Partizan managed to take three points away from Germany against Augsburg after an Andrija Zivkovic double, despite ending the game with ten-men.
Napoli continued their good start to the Europa League with a 2-0 win away at Legia Warsaw, after goals from Dries Mertens and Gonzalo Higuain, while undefeated Bundesliga side Borussia Dortmund were held to a 1-1 draw at PAOK.
Like fellow Italian side Napoli, Fiorentina were also away winners on matchday two, with a comfortable 4-0 victory at Portuguese side Belenenses.
Player of the Night: Franco Di Santo (Schalke)
Team of the night: FC Midtjylland
Goal of the Night: Ebenezer Assifuah (FC Sion)