Atletico Madrid goalkeeper Jan Oblak was the hero as the Spanish side reached the UEFA Champions League quarter-finals for the fourth year in a row after drawing 0-0 with Bayer Leverkusen in an open last-16 second leg.
Liverpool's first loss of the season means they cannot finish the campaign unbeaten to match Arsenal's 'Invincibles' of 2003-04.
A summary of Tuesday's action in the Premier League.
IMAGES from the English Premier League matches played on Saturday.
IMAGES from the Premier League matches played across England, on Saturday.
Images from the English Premier League matches played on Saturday
Atletico Madrid substitute goalkeeper Antonio Adan saved three penalties before blasting home the winning spot-kick as the Europa League champions edged out Arsenal after the sides drew 1-1 in their International Champions Cup opener in Singapore on Thursday.
Manchester City came out on top in an epic Champions League battle against Monaco whereasAtletico Madrid beat hosts Bayer Leverkusen 4-2 in a topsy-turvy encounter.
World Cup winner Neuer, who has been the Germany number one for more than eight years, has not played a single official game since breaking a bone in his foot back in September but Koepke said he was fully on track for the tournament in Russia.
The Germans have lost just once in 23 games since their Euro 2016 semi-final defeat, cruising through the qualifiers with 10 wins in 10 matches.
IMAGES from the English Premier League matches played on Saturday.
IMAGES from the Premier League matches played on Sunday.
IMAGES from the Premier League matches played on Saturday
It will be a poignant evening, with both games -- City vs Arsenal and Aston Villa vs Sheffield United -- played inside empty stadiums and marked before kickoff by a minute's silence for the more than 40,000 people to die of the virus in the UK.
Champions Bayern Munich comfortably beat Bayer Leverkusen 3-1 in the Bundesliga season opener on Friday to lay down a marker as they eye a record-extending sixth straight German league title.
Athletic Bilbao beat Barcelona 4-2 at home to knock them out of the Copa del Rey
IMAGES from the Premier League matches played on Saturday.
The Bundesliga was in danger of turning into another one-horse race on Sunday after second-placed VfL Wolfsburg were held 1-1 at home by promoted Paderborn, leaving titleholders Bayern Munich nine points clear at the top.
IMAGES from the Premier League matches played on Saturday.
A round-up of Sunday's action in the Premier League.
Bayern Munich went top of the Bundesliga with a 1-1 draw at Bayer Leverkusen on Saturday as rivals Borussia Dortmund slumped to their first defeat of the season with a 2-0 reverse at Borussia Moenchengladbach.
Wenger departed in May after 22 years in charge having endured a barrage of criticism in the latter part of his reign for a tactical approach that resulted in 14 seasons without a Premier League title.
IMAGES from the EPL matches played on Wednesday.
Images from the English Premier League matches played on Saturday.
Images from the English Premier League matches played on Sunday night.
The result leaves Arsenal in fifth place on 15 points, two behind Leicester City and Chelsea, while Sheffield United moved into ninth on 12 points.
A summary of Sunday's action in the Premier League.
Images from Sunday's action in the Premier League.
IMAGES from the English Premier League matches played on Sunday
IMAGES from Premier League matches played on Saturday.
Germany coach Joachim Loew has named four talented youngsters, including three uncapped players, in his preliminary 27-man squad for Euro 2016.
Tottenham Hotspur climbed to third with a 3-1 win over Southampton while Chelsea hung on to fourth spot, above Arsenal on goal difference, despite a 2-1 defeat at Wolverhampton Wanderers.
IMAGES from the English Premier League matches played on Sunday.
Manchester City now need, at most, 11 points from their remaining seven matches to secure their third Premier League title in four seasons.
Premier League champions Liverpool maintained their 100 per cent start to the season with a 3-1 win against Arsenal at Anfield on Monday leaving them level on nine points with pacesetters Everton and Leicester City.
Arsenal are eighth, seven points adrift of fourth-placed Chelsea, while Norwich remain second from bottom.
The result leaves Ole Gunnar Solskjaer's United in 10th with nine points, their worst start after seven games for 30 years, and they have won just one of their last six league games.
Unai Emery begins the task of steering Arsenal into a brave new post-Arsene Wenger world.
Arsenal fielded a strong team with Ozil installed as captain and the Premier League side soon took control against weakened opposition, given the time and space they will not be afforded when the domestic campaign kicks off in August.
Bayer Leverkusen beat a second-string Bayern Munich 2-0 on Saturday to move up to third in the Bundesliga and get back on course for an automatic Champions League spot with three matches left in the season.