Following the Saturday injury, fans around the world took to social media to send Shaw goodwill messages as he reworks his journey back to fitness.
Shaw was left unconscious after colliding with Spain defender, Dani Carvajal early in the second half.
The Real Madrid right-back requested Shaw's mobile number from his worldwide team-mate to check on his condition after he had to be taken off on a stretcher following several minutes of treatment from medical staff.
He tweeted: "Thank you for all the love and support I am doing fine and am in the best hands".
Manchester United have scored six goals this season.
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After struggling last season to convince Jose Mourinho he was worth a place in the team, he has started the current campaign in impressive fashion and his contribution on Saturday before his injury will have impressed Southgate.
Marcus Rashford score for England while Saul Niguez and Rodrigo secured victory for the Spanish side.
The Spanish outlet claim that De Gea couldn't fully enjoy the post-match praise he received because he was too anxious about his teammate.
However, his latest transfer plans, may just indicate that Rose's reprieve is only to be a short-term fix, as if Spurs do sign another left-back then the England international's future will come into question again.
A number of supporters and players wished Shaw well and hoped he would recover soon from the knock.