The Nerazzurri needed to match Borussia Dortmund’s result against Slavia Prague when they hosted Barcelona at San Siro on Tuesday in order to qualify for the last 16.
Barcelona took the lead through Carles Perez in the 23rd minute effort
Lukaku’s long-range drive gave Inter hope just before half-time.
It was Barca who had the final say, however, when 17-year-old Ansu Fati became the youngest goalscorer in Champions League history late on to secure a 2-1 win for the visitors.
Dortmund’s 2-1 home victory over Slavia ensured that they joined Barca in the knockout stages, with Inter set for a return to Europa League football in 2020.
Shaw, who played with Lukaku for two seasons before the centre-forward moved to San Siro in August, aimed a dig at his former team-mate on social media after the match.
Hours before Inter kicked off against Barca, Lukaku tweeted an image of himself in high spirits during a training session, with the caption “UCL”.
In the wake of Inter’s Champions League failure, Shaw wrote “welcome back” above the Belgian’s original post, sarcastically mocking the striker.
”It’s not the first time Shaw and Lukaku have exchanged Twitter barbs after the Belgian striker poked fun at the England full-back’s lack of speed during a pre-season test.
There is now a chance that United could end up facing Inter at some point during the Europa League knockout stages, which would see Lukaku return to Old Trafford to face Shaw and the rest of his old colleagues.
Inter will look to bounce back from their deflating Champions League experience when they travel to Fiorentina on Sunday.
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