Short was sat in the stands at the Stadium of Light for the first time since August for Saturday's goalless draw with Burnley and is unlikely to have been impressed with what he saw from Moyes' men.
Billy Jones and Sebastian Larsson both missed good chances for the Black Cats before Burnley keeper Tom Heaton stepped up to deny Fabio Borini three minutes from full-time, the draw leaving the north-east outfit seven points from safety at the bottom of the table.
Short's appearance has sparked speculation over Moyes' future at Sunderland, the Scot having struggled since taking charge in the summer, while recording just one league win in 2017.
Short has made managerial changes at this stage in the season before, getting rid of Martin O’Neill and Gus Poyet in March with Sunderland staying up on both occasions.
However, Moyes remains unconcerned about his future as manager.
Moyes said: "I spoke to him [Short] today. I suppose if you own a football club you are entitled to come and watch it -- he is allowed to do that. I saw him this morning and he is entitled to come along but it is all good.''
Having failed to beat a side without an away win all season at home, Moyes admits he needs to reassess where the points needed to keep Sunderland up are going to come from in the rest of the season.
Moyes added: "It's not enough - it would have been down as one of the wins in my book, so now we have to turn one of the draws I had down into a win.
"The players know exactly how much it means and they know we have to win. We emphasised how big the game was and they didn't lose - but three points was really what we needed."