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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.