The Dutchman has faced fierce speculation over his future in recent months, with increasingly frequent reports suggesting that Jose Mourinho is being lined up for the Old Trafford job.
A 2-1 defeat at the hands of relegation-threatened Sunderland on Saturday leaves the Red Devils six points adrift of the top four, but Moyes warned that United simply have to qualify for the Champions League, be that via the Premier League or by winning the Europa League.
"I knew Manchester United need to qualify for the Champions League. I think Manchester United need to be there. They are a club of status and want to be at that level, if not more. They want to be winning it if they can, never mind qualifying for it. That's what happens at Manchester United. It's that level," Moyes told Sky Sports News.
"There's so much media attention on Louis van Gaal just now. When I lost my job, he was lauded by everybody in football - by you people, the media and everybody else. Now many of you are the ones saying he should lose his job.
"If you go to Manchester United, that's what you get. You get an awful lot of media attention. But I still believe I was the right person to take the job."
United take on FC Midtjylland in the first leg of the Europa League last 16 on Thursday.