Lindegaard, who joined United from Norwegian club Aaleslund in 2010, is currently the understudy to first-choice shot-stopper David De Gea at Old Trafford.
The Denmark international has not featured in United's Premier League campaign so far this term, making just two appearances, in the Capital One Cup and the FA Cup.
United boss Moyes has been under intense scrutiny, with the defending champions currently seventh in the top flight, 11 points off the pace of league leaders Arsenal.
Lindegaard insists Moyes is not the one to blame but claims playing for a club the size of Manchester United comes with great responsibility and the 29-year-old explains there is no let-up in intensity at Old Trafford.
"Many players have got a lot of responsibility and would need to get a break," Lindegaard told TV3 Sport.
"But that is not possible at a club like Manchester United. Regardless who is the coach, this tough time would have come in any case."
Despite enduring a disappointing start to the season, Lindegaard believes United have the necessary credentials to return to title-winning form.
"I believe that we will get things back on track and United will blossom again," he added.
"I cannot imagine that Manchester United will not be a top club and a top brand in the future."