Milan travel to the Nou Camp on Tuesday with a 2-0 advantage from last month's first leg, when they successfully outmaneuvered Lionel Messi and company at the San Siro.
However, at the same stage last year Milan romped to a 4-0 victory at home to Arsenal only to suffer a nail-biting second leg as Arsene Wenger's team fought back to lead 3-0 by halftime in London, before the Italians held firm in the second half.
"We have a lot to lose," Milan captain Ambrosini told a news conference.
"We are in a good position, but that doesn't guarantee us anything in any game. Last year, after the 4-0 against Arsenal in the first leg they almost dumped us out into the street.
"We have to make the most of the result we have, and last year was an episode that should serve as experience."
Milan also hold the record for the biggest first-leg victory overturned in the Champions League era, losing 4-0 at Deportivo La Coruna in the 2002-2003 quarter-finals, having won 4-1 at home in the first leg.
Coach Massimiliano Allegri was not expecting a repeat performance, but still preferred to play his hand as the underdogs.
"It would not be a disaster to go out at this stage because no one expected us to arrive here with a two-goal advantage," Allegri said.
"Everyone thought it would be an easy ride for Barca. We should forget about the 2-0 in the first leg. Now, two out of three results are good for us."
Allegri predicted a similar game to last month's but said his side would need to play much better this time.
"They will put us under a lot of pressure, but we will need to be as serene as possible. We know we have to try and score a goal and, if possible two, to feel comfortable," he added.
"They are so good at generating chances that when you play against them you have to be very good in defence and much better in attack.
"Your percentage possession is so low that the chances to score are very few.
"With a little luck and playing the way we know how, we can make it through to the quarter-finals."
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