Inter needed all three points to stand a chance of progressing into the knockout round and hoped results in the group’s other game favoured them.
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But it was not to be as Barcelona, without star skipper Lionel Messi, won with goals from Carles Perez in the 23rd minute and upcoming star Ansu Fati in the 87th minute.
Former Manchester United striker Romelu Lukaku had drawn Inter Milan level on 44 minutes.
In the other game in the group, Borussia Dortmund beat visiting Slavia Prague 2-1 to advance to the round of 16.
Barcelona top the group on 14 points while Dortmund are second on 10 points.
Inter, a three-time Champions League winners, finished third on seven points and will now feature in the Europa League.
In Group H, last season’s semi-finalist, Ajax, failed to qualify for the knockout stage following their 1-0 home loss to 10-man Valencia.
Ajax needed at least a draw to advance, but it was not to be as a 24th minute strike by Rodrigo ended their hopes.
Valencia were reduced to 10 men following the sending off of former Arsenal defender Gabriel Paulista in the 90th minute.
Up next for Ajax is the Europa League after finishing third in the group on 10 points.
At Stamford Bridge, Chelsea picked up the needed win to advance after beating already eliminated Lille 2-1.
Tammy Abraham and Cesar Azpilicuerta got Chelsea’s goals in the 19th and 35th minute respectively, while their former player, Loic Remy, scored Lille’s goal on 78 minutes.
Valencia emerged winners of the group on 11 points, the same point with second placed Chelsea but edged it on superior head-to-head record.
In Group E, Liverpool put any doubt of qualifying for the next round away with a comfortable 2-0 away win against Salzburg.
After a goalless first half, Naby Keita opened scoring for the reigning Champions League holders on 57 minutes before Mohamed Salah made it 2-0 On 58 minutes.
Napoli joined Liverpool in the next round after thrashing Belgian club Genk 4-0 in Naples.
Liverpool top the group on 13 points and Napoli finished in second place after amassing 12 points.
And in Group G, Bundesliga side RB Leipzig and French Ligue 1 outfit Lyon are the two sides that made it to the next round.
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