With Renan Lodi's first-half goal putting Atleti up 2-1 on aggregate, United eventually went out tamely as they struggled to create much of substance while chasing the result.
According to former United centre-back Ferdinand, the biggest difference between the two teams was not on the pitch but rather with Ralf Rangnick and Diego Simeone in the respective dugouts.
"The difference between the two teams, the Atletico team, they had a group of reliable men, reliable men who would go out there and do anything the manager asked of them," Ferdinand said.
"They understand the job at hand and they work together as a team. Whereas the other team, Man Utd, they’re looking at each other like, 'Who's going to pull us out of this? Who's going to pull the magic trick out of the hat?'
"It's not about the team getting through this. It's a moment of brilliance from an individual and it's a very different way of working."
Ferdinand hedged his comments, though, saying the club needs to patiently progress when they bring in a manager, a process which has reportedly already begun behind the scenes.
"Once you get the manager, getting the right person, you're talking minimum of two, three years before you can think about challenging, and with Manchester City and Liverpool it's a high bar," Ferdinand said.
Scholes delivered a particularly blunt assessment, asserting interim manager Rangnick is not meeting expectations with the squad he has at his disposal.
"The coach is a massive part of it, getting a proper coach. This isn't a terrible group of players, if you give them structure and a way of playing, there's some real talent in this squad. It's not as talented as the teams above them, we know that," he said.
"The very first thing this club needs to do, to get anywhere near winning anything, is get a proper coach. Get a coach that suits them and give them a couple of years to build a squad that will challenge.
"Atletico are not a better team than Man United, but they've got a better coach. If he [Simeone] was coaching Man United, they go through that game.
"What it comes from is leadership. It comes from a coach who demands that and will get that out of his players. I don't want to keep having a go at this manager. He seems real nice, I love his interviews, he's very honest, but how he was chosen to be manager of this club – whether it's for six months, six weeks, six games – I don't know."