Red Devils boss Sir Alex Ferguson was left fuming by his side's last-16 defeat to Real Madrid in midweek, highlighting Nani's "astonishing" red card as the turning point in the game.
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He told reporters: "United will now concentrate all their strength to win the championship and it was hard enough for us before this game against Madrid.
"It was better for us that they stayed in the Champions League."
The 48-year-old also voiced his disagreement with Turkish referee Cuneyt Cakir's decision to send Nani off for a high challenge on Los Blancos defender Alvaro Arbeloa.
"I can see why Ferguson was frustrated," Mancini explained. "It was the same thing that saw [Vincent] Kompany sent off against Manchester United in the FA Cup last year.
"This was a big mistake and for me Nani did not deserve a yellow card. Even in Italy it would be nothing because Nani tried to take the ball."