Having lost the first leg 2-0 in Madrid, Atletico were facing an uphill struggle and could only win 1-0 away.
Inter Milan beat CFR Cluj 2-0 in their second leg to book a last 16 tie with Tottenham, whose last minute equaliser in Lyon gave them a 3-2 aggregate win.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.