The highly rated 18-year-old defender suffered a knee injury that forced him off during the 4-3 victory over the Spanish side on Saturday and had to be helped down the tunnel.
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"In principle it is his knee but we still need to know what the doctors will say," he told the post-match press conference.
"He has a problem in his ligament but we need to see what the doctors diagnose.
"We will have to see. He had to leave the stadium and the pitch and hopefully the problem is not as big as it looked and he will be okay."
Shaw was an integral part of the south-coast side's first season back in the top flight last term, making 25 appearances as the club finished 14th.
His performances have reportedly attracted attention from a host of Premier League rivals - including Chelsea and Manchester United - but the youngster committed his future to the club by signing a new five-year deal in July.