The Latics man fell awkwardly as the two players came together in the 32nd minute at Anfield, with manager Roberto Martinez confirming after the match the nature of the injury.
"To Ben Watson I didn't realise it was serious as that ill be praying for a speedy recovery mate ill have you in my prayers every day #sorry," an apologetic Sterling wrote on Twitter.
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"I haven't seen the challenge back but I don't think any of the players were looking at each other," he told reporters.
"Both were looking at the ball, it's a real accident. It's a nasty collision."