RIO DE JANEIRO -- Paulinho equalized late on with a volley for Brazil to draw 2-2 with England on Sunday and prevent the 2014 World Cup hosts from losing their opening match at the revamped Maracana stadium.
But Paulinho's goal in the 82nd minute ensured England would fail to replicate its victory over Brazil at Wembley Stadium four months ago.
"You want to be able to close out the game, so in that sense we are disappointed," Oxlade-Chamberlain told British broadcaster Sky Sports. "But the boys showed great passion and great fight ... it's tough coming away in the heat."
About 66,000 fans were in the Maracana, which has undergone renovations worth an estimated $1 billion to turn it into a 79,000-seat venue.
The game was thrown into doubt last week when a judge ruled the stadium was unsafe, but the order was overturned.
The confusion reflected the various cost overruns and delays in building stadiums in Brazil ahead of the Confederations Cup, which starts in two weeks as a warm-up for the 2014 World Cup.
Brazil's prospects of replicating its 2002 World Cup success are currently looking distant, with Luis Felipe Scolari's side having won just one of its past six games.
Star Brazil forward Neymar, who heads to Barcelona after the game for his official presentation after signing a five-year deal at the Spanish champions, could find no way past goalkeeper Joe Hart.
Hart also denied Hulk and Filipe Luis in quick succession in the first half, and blocked a powerful shot from Oscar.
"We didn't play well in the first half, but we battled and dug deep," Hart said.
Brazil goalkeeper Cesar denied Theo Walcott twice in a first half dominated by the hosts. Their breakthrough came after the break when Hernanes hit the crossbar and Fred pounced from close range to stab the ball into the net.
England's fortunes turned after Oxlade-Chamberlain replaced Glen Johnson on the hour, 29 years after his father Mark Chamberlain appeared for England in the same stadium.
It took just seven minutes for Oxlade-Chamberlain to score. A string of passes led to Rooney knocking the ball back for the Arsenal winger to crack a shot past Cesar.
"He ripped it up ... he smashed us back into the game," Hart said of Oxlade-Chamberlain.
As Roy Hodgson's side gained in confidence, Rooney took on the Brazilian defense, charged into space from the left and curled the ball into the top corner.
But Paulinho made sure England failed to follow up its 2-0 win in Rio in 1984, volleying past Hart from Lucas Moura's cross.
"Some draws can be labeled victories and some draws can be labeled defeats," Hodgson said. "I'm a bit disappointed today, and we were playing so well in the second half I thought we might just hold on to it. But we were scotched by a wonder strike."