Should they all fail, it would mark the first time since 2005 that a Spanish side had not reached the last eight, when Barca and Real Madrid fell in the last 16 after Valencia and Deportivo La Coruna were eliminated in the group stage.
Barca are in the most precarious position after a superbly organised Milan successfully repelled wave after wave of attacks from the 2011 winners and stopped the free-scoring Lionel Messi from producing a single shot on target.
Barca's great rivals Real drew 1-1 at home to Premier League leaders Manchester United in their first leg last week, meaning they have to score at Old Trafford to keep their dream of a 10th European crown alive.
Valencia lost 2-1 at home to big-spending Ligue 1 side Paris St Germain, while Malaga, making their debut in Europe's elite club competition, were beaten 1-0 at Portuguese club Porto.
"Suspense for the Spanish Champions League teams", was the headline in Marca sports daily on Thursday.
Barca were furious about Milan's opening goal 12 minutes after halftime at the San Siro after the ball appeared to strike Cristian Zapata's arm before Kevin-Prince Boateng swept it past Victor Valdes.
However, they could have no complaints about Sulley Muntari's fine volleyed effort in the 81st minute and they have to score at least twice against the Italians at the Nou Camp on March 12.
There was a familiar pattern to Wednesday's game, with Barca stroking the ball around outside Milan's penalty area but lacking the decisive final ball.
It was a similar story when they were knocked out by eventual winners Chelsea in last season's semi-finals or at the same stage in 2010 by Milan's city rivals Inter.
World Player of the Year Messi looked a shadow of the man who has top-scored in the competition the past four seasons, while Cesc Fabregas struggled to get into the game before being replaced by the equally ineffective Alexis Sanchez just after the hour.
Normally the source of much of Barca's attacking verve, their two dangerous wingbacks, Jordi Alba on the left and Daniel Alves on the right, were well marshalled by Ignazio Abate and Kevin Constant respectively.
The statistics tell the story: Barca had 65 percent possession, with 674 completed passes to Milan's 261, but managed only two shots on target compared with their opponents' six.
They had not lost by more than one goal since a 3-1 King's Cup defeat at Real Betis in Jan. 2011 and had not been defeated by more than one goal in the Champions League since going down 3-1 to Inter at the San Siro in the first leg of the 2010 semi-finals.
"This stadium is always tough," assistant Barca coach Jordi Roura, standing in for Tito Vilanova as he recovers from throat surgery, told a news conference.
"Milan had their plan," he added.
"They deployed a lot of players at the back, with a good deal of order and commitment.
"It was hard for us to show our usual fluidity and depth to get through to the opponent's goal as easily as on other occasions."
Roura criticised the state of the pitch, which he described as "a potato field" unfit for a Champions League game.
"It's true that it's difficult for us to play our game on such a pitch and that makes things much tougher but excuses are pointless," Alves told reporters.
"We were not up to scratch in general and that is down to the merits of our opponents and our failures, we have to improve," the Brazil international added.
"The result is a tough one but nobody is gifting anything. We have to fight, go after the game (in the return leg) and work hard. To get through we'll have to improve."
Barca host Milan on March 12, Real play at United on March 5, Valencia are at PSG the following day and Malaga host Porto on March 13.