Xavi was amongst a number of players who claimed Barca's chance had gone with a 2-2 draw at home to Getafe two weeks ago, but a remarkable end to the tightest title race in years in Spain – in which the top three have failed to win in their last seven combined games – has gifted the Catalans a second chance to be champions.
"We thought that we didn't have a chance and perhaps we threw the towel in too soon," said the Spanish international.
"We thought the league was lost, but these things happen in football and now we have everything in our favour to win. It is a very important title and we need to be united. It is a historic opportunity. It will be a spectacular finale."
Victory would secure an eighth league title for Xavi and a seventh for the departing Carles Puyol and Victor Valdes, but he insists the most decorated squad in Barca's history still have the hunger to succeed.
"We have a great generation of players. This is a unique match, a unique opportunity which may never come round again.
"It would be the icing on the cake for this generation to play in such a vital match."
However, to win the league Barca will have to do something they have failed to in five previous meetings this season and beat Diego Simeone's exceptionally well-organised Atletico side.
Barca have managed just two goals in those five encounters and have yet to go in front in any of them.
Neymar is the only Barca player to have scored against Atletico in those five encounters and the club are hopeful that the Brazilian will be able to make an impact after being given an all-clear by the medical staff.
Gerard Pique and Jordi Alba have also returned to training, but the match is likely to come too soon for both Spanish internationals.
Atletico are hopeful their own Brazilian-born star striker Diego Costa will be fit after he missed last weekend's 1-1 draw at home to Malaga with a hamstring problem.
A La Liga and Champions League double would seal the best season in Atletico's 111 year history, but defender Filipe Luis insists they are enjoying the experience rather than feeling under pressure.
"We aren't under pressure, we have a great responsibility,” he told the club’s website.
"It hasn't been easy, but we have got here with a lot of hard work and now we need to finish off the season in style.”
Ronaldo fit to face Espanyol, says Ancelotti
Real Madrid's top scorer Cristiano Ronaldo has recovered from a series of niggling injuries and is fit to play in Saturday's La Liga game at home to Espanyol, said coach Carlo Ancelotti on Friday.
"Ronaldo is fine, available, and tomorrow [Saturday] he will play the match," Ancelotti told a news conference.
Only three players, goalkeeper Diego Lopez, centre back Pepe and long-term injury casualty Jese are unavailable for the game at the Bernabeu, added the Italian added.
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