Sunderland drew 2-2 with West Ham at the Stadium of Light and remain bottom of the Premier League standings, nine points from safety.
Moyes is not believed to be in danger of losing his job, even if Sunderland go down, as the North East club have faith in his managerial ability.
The Scot said, "The supporters have been fantastic. No-one is happy at the football club at the minute because of the position we are in".
There was major concern for the Black Cats as Jones was took off with a suspected neck injury, that brought around 10 minutes of extra-time, and Sunderland managed to grab their point right at the end of normal time.
Wahbi Khazri's unlikely first equaliser, direct from a corner, softened the anger inside the ground.
The Sunderland manager's arrival on the touchline in the 20th minute of Saturday's home 2-2 draw against West Ham was greeted with a chorus of boos and chants of "we want Moyesy" out from the South Stand.
West Ham United are all but safe and have little other than pride to play for.
Sunderland boss David Moyes hopes that Wahbi Khazri will have an impact in the final weeks of the season - and insisted that his exclusion has never been about a lack of work-rate.
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Without a home league win since mid-December, Sunderland have long seem destined for the Championship but, paradoxically, Saturday represented the team's best performance for some time.
"I'm disappointed with both goals, but not disappointed generally with the play".
A seventh defeat in eight league games loomed for Sunderland when James Collins headed past Jordan Pickford immediately after the restart but there was some late joy for the hosts.
"We did it last season, the three of us up front - me, Wahbi and Jermain Defoe - we did well". We could easily have lost 2-1 but gained a point on those teams around us. We probably haven't defended either goal of well as we should have done.
It's the first time the crowd have turned on Moyes, but he told reporters after the match "they deserve to take their frustrations out on someone".
"I just keep in mind to myself that I think I have got the third or fourth best win record in the Premier League".
The Frenchman was inserted back into the side for his 16th appearance of the season against West Ham and made an instant impact.