"I have to control myself a lot, but sometimes it's a reflection of how our club is at the moment," Martinez told Amazon Prime.
"We had a fantastic season last season, and now we expect more from the top, from upstairs, to bring in more players to compete because many teams have brought in many players as well."
I have to control myself a lot, but sometimes it's a reflection of how our club is at the moment
Lisandro Martinez
While Martinez has been praised by some United fans, particularly on social media for his comments, Carragher has taken a different approach.
"It doesn't do anybody any good at all, and they will be the story now for the next few days all about this,” Carragher said on CBS Sports.
"Every set of supporters don't like the suits or the guys upstairs, so United fans will lap this up and think it's great. 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 last season', they didn't. A manager got sacked last season. Sacked.
"They finished third because they had no cup games. They got knocked out of the cup competitions very early. The reason they finished third is Liverpool and Chelsea were that bad as well.
"Now we're seeing the real Manchester United this season. They were awful again tonight.
"And him as well, when he's talking at the start of this season - I think he's a good player, by the way, he's a World Cup winner, I get that - he's had an awful start to the season. Awful. Really poor.
"And yeah, people are lapping it up, Manchester United fans will. That does nobody any good at all."
Michael Carrick and Youri Tielemans were asked about Martinez’s comments post-match but side-stepped the question, though United legend Rooney was critical of the Argentina international.
Speaking on Amazon Prime, Rooney said: "It's a difficult one because I always used to think I was outspoken as a player and you want to have your opinion.
"I think he has maybe gone a bit too far. That's for the manager, and that should really stay internal.
"The fans want to hear the players speak; they want to hear the players care, so you can clearly see he cares and he wants the team to invest more money, and more players, and to do that he is probably one of the players who is out the door through his performances. His performances haven't been good enough.
"But it looks like that was a bit of an agenda; he's wanted to say that, because that doesn't mirror the performance. I thought the performance was better.
Rant: Lisandro Martinez
Getty
"It's a bit disrespectful to his team-mates as well. He is disrespecting his team-mates because he's saying the team isn't good enough.
"Players have conversations with the manager, the manager has conversations with the board, but that interview is not going to help the situation the club are in at the minute.
"That's going to bring a greater noise around it; the players are not happy, they're not settled, they don't trust in their team-mates. That's not going to help at all."