Barca defender Carles Puyol will be missing from the first leg after picking up a yellow card in the 1-0 win over Schalke.
United defender Nemanja Vidic missed Wednesday's game against Roma because of a knee injury but Ferguson added: "Hopefully by then we will have him back. If we have a full squad then we will have a very good chance."
Roma were handed a lifeline in their tie with United when referee Tom Henning Ovrebo awarded the Italian team a penalty following a challenge by Wes Brown on Mancini.
However, Daniele de Rossi smashed the spot-kick comfortably over the United crossbar.
Ferguson said of the ruling: "It was a bad decision. Wes Brown got the ball, no doubt.
"We are just pleased to be through. We had to play well but it was a European quarter-final against the team lying second in Italy and you expect them to play a bit.
"Our home record has been very good and is something to be proud of and it will have to remain so because European football is difficult."
We've two unbelievable games of football to look forward to against Barcelona
United's defeat of Roma was their 11th straight win at home in the Champions League - a new record for the competition.
Roma coach Luciano Spalletti conceded that the best team had won the tie but stated: "We put in a good game and a good performance.
"We had to take one or two risks. It was important to exploit chances when we actually created them but we didn't capitalize on them.
"If we had it would have changed the face of the game."
Gary Neville came on as a late substitute for United - his first appearance since he picked up an ankle injury against Bolton on 17 March 2007.
"I hope for this season I can come in and play a small part because it's frustrating missing run-ins," said the defender, who also believes the tie with Barca is one to be relished.
"We have two unbelievable games of football to look forward to, two football clubs who play the game the right way and they will be unbelievable occasions to be part of," he said.
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