Martinez famously ripped into United this week as he staunchly defended Michael Carrick and ripped into technical director Jason Wilcox over how the club is being run.
Martinez added: "Last season we created a base to build an amazing team. It's annoying and disappointing to come here and I'm not seeing my team get an amazing result here."
The loss to Atletico only adds to the fact that the club are out of the Premier League title race and the EFL Cup as the season shapes up to be another disappointment.
Carragher says Martinez comments are "awful"
Martinez's view has been echoed by many fans but Carragher spoke up on his comments, revealing that nobody can be shocked by United's downfall.
"Doesn’t do anybody good at all, and they will be the story now for the next few days all about this. Every sets of supporters do not like the suits, the guys upstairs, so United fans will lap this up and think it’s great," Carragher said on CBS Sports.
"I think it’s awful that he’s come out and said that right now, I do. And when he’s saying ‘we had a fantastic season’, they didn’t. A manager got sacked last season; they finished third because they had no cup games, and they weren’t in Europe.
"The reason they finished third is because Liverpool and Chelsea were that bad. Now we’re seeing the real Manchester United this season. The reason they didn’t buy players in the summer is that for the last four or five years, since Martinez has been there, I think they’ve been in the Champions League once (this season).
"So for every season you don’t get Champions League money, and every season Man United are spending £200 million, sooner or later it has to stop because the money’s not there."
The Red Devils finished third in the Premier League last term to seal a Champions League return for the first time in three years. This came after the side sacked managers in the past two seasons as they undergo constant change which Martinez, as well as many other suppoters are not happy with.
Martinez, who already has links to Atletico, has one year left on his United contract and has yet to agree an extension.