In the 39th minute of the match, in which Shelvey made his debut following a £12m transfer from Swansea City, the midfielder appeared to barge Valencia over as play continued.
The incident was not seen by the referee and was therefore referred to the Football Association's independent video review panel, which is manned by three former referees.
The panel decided that the incident did not warrant a red card and that no further action will be taken against the former Charlton and Liverpool midfielder.
The England international played a part in both his side's goals in a debut which drew praise from Newcastle manager Steve McClaren.
"Jonjo showed his quality," McClaren told Sky Sports after the game. "In our team we've got good players around him and he will get better and better. But I thought his performance was very good."