Moyes succeeded new England coach Sam Allardyce at the Stadium of Light in July but has endured a difficult transfer window and a slow start to the season during his first two months in charge.
The Wearsiders have taken just one point from their opening four games of the league campaign and suffered a demoralising 3-0 defeat at home to Moyes' former club Everton on Monday.
Another difficult fixture at Tottenham on Sunday awaits and Moyes is demanding more of his underperforming players. Speaking at his news conference on Friday, he said: "The players have to lift their levels. They have to show they are good enough to play at this level.
"It's always the manager. I will take responsibility for the job but you have to think 'come on' ... the players have had a lot of managers here. It's time to start standing up for what you can do. You [the players] are better than what you showed the other night."
Moyes, who could have Lee Cattermole and Steven Pienaar back for the trip to White Hart Lane, denied suggestions the Sunderland post represented his biggest challenge in football, instead pointing to the size of the task that faced him when he took over at Everton.
"No, my biggest challenge was to take a club from the bottom end of the Premier League and make them a top-six club," he said. "I did that and we'll do this one as well."
One piece of good news for Sunderland during another underwhelming week was Lamine Kone's decision to sign a new, five-year contract.
The Ivory Coast international's future was the subject of much debate during the window with Sunderland rejecting a bid from Everton for the former Lorient defender.
Moyes said: "It was definitely a distraction for us all during the window but we've got it done now.
"He's an important player. We've rewarded him and we are looking for big performances from him. He now has a contract where you expect him to be a key player in every game."
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