Sir Alex Ferguson singled out Nani for giving away possession at a crucial time, which led to Chelsea scoring the equalizer in normal time, with the Blues then going onto win the tie 5-4 after extra time.
Nani's future became more uncertain after the United manager bemoaned the winger's careless play, even if the likes of Alexander Buttner and Scot Wootton might have given away needless penalties.
Nani, who scored United's third goal against Chelsea, is yet to agree on a new contract and has been linked with a move away quite often in the last few months. The Portuguese winger's current deal expires in 2014.
"We gave the ball away for the third goal having been in complete control of the match at that point," Ferguson said. "All we needed to do was see the game out with good possession.
"Nani is experienced but he's a player who wants to beat men and I often discourage him from that. In that situation, if we'd kept the ball at the corner flag, the game's over. Nani decided to try and beat a player, lost the ball and we ended up conceding a penalty kick.
"It's disappointing (to go out). Some of our football was terrific.
"We had a lot of attacks and nothing came of them, and their counter-attack was very good, but if you're winning 3-2 in the final seconds of the game then you should see it out.
"We've only got ourselves to blame really."
Ferguson admitted he had taken a gamble starting two rookie center-backs in Wootton and Michael Keane, with the former not only conceding the late penalty, but also making the mistake which led to Daniel Sturridge scoring Chelsea's fourth goal in extra time.
"We took a gamble in terms of the centre-backs," Ferguson added. "It's very difficult because one's 19 (Keane) and one's 20 (Wootton). It's not easy.
"You can always get away with playing young forwards but playing young central defenders away from home, in a game of that magnitude, is going to make for a difficult night. That's how it proved.
"They'll learn from the experience but nonetheless it was a hard night for them.
"From a spectator's point of view it was a terrific game of football. You're getting your money's worth with nine goals, there's no doubt about that."
Ferguson also reserved special praise for the ageless Ryan Giggs, who scored two goals in the entertaining tie. "He is an example to all the players on that pitch, including the Chelsea players," Ferguson told the club's official website. "In Ryan we saw a player of absolutely unbelievable proportions in terms of playing 120 minutes when he's 39 next month.
"He was absolutely magnificent and is a real credit to himself and the game."
