Michael Carrick’s side were 1-0 down inside the first minute thanks to a goal from Atletico midfielder Pablo Barrios at the Wanda Metropolitano.
Leny Yoro was shown a straight red card for a last-man challenge on Jonathan David in the second half, and Atletico fully capitalised on their numerical advantage and doubled their lead through Ademola Lookman to secure all three points.
United have just two wins across their nine games in all competitions so far this season, with pressure mounting on Carrick just months after guiding them to a third-place Premier League finish.
Speaking to Amazon Prime after the game, Martinez didn’t hold back on what he believes the reason behind their disappointing start to the season is.
"Really poor. Really poor. I have to control myself a lot but sometimes is a reflection of the mirror of how is our club at the moment," he said.
"We did a fantastic season last season and now we expect more from the top, more players to compete because many teams bring many players as well. Atletico have an amazing team and they deserve to win today.
"I expect more (investment). 100%. I expect more from our technical director (Jason Wilcox). I have to be honest, as players we have to do more but it is also important when you make a strong squad to be ready for this kind of night."
"Last season we did everything; we created the base to create an amazing team. It is annoying, disappointing coming here, and I am not seeing my team trying to get an amazing result here.
"(Michael Carrick) does his best. Every season is different. You can't stay with what you did last season. The teams knows how you play, they know every detail, if you don't change next season is a big problem.
"You can't keep changing, changing, changing the manager. What about other areas? I can't say more.
"Tonight it is easy to say the coach, easy to say the players, but also we have to see other areas."
Man Utd face rivals Leeds in the Premier League on Sunday.