Alex Ferguson's side, whose elimination by Real Madrid on Tuesday has left them with only domestic matters to focus on, had some unlikely supporters of their European campaign in Manchester City.
"It's worse for us because I think now they put all their strength into the championship," Mancini, whose side trail United by 12 points, told a news conference.
"I think for us it was better they stayed in the Champions League. They would have played an important game every three days, it is more difficult."
Before the Manchester clubs get back to their league duel, they turn their attention to the FA Cup, with United hosting Chelsea in the quarter-finals on Sunday the day after City entertain Championship (second tier) Barnsley.
Mancini will be without injured forward Sergio Aguero, who did not play in Monday's 1-0 league win over Aston Villa because of a knee problem, and captain Vincent Kompany, who has been absent with a calf injury since late January.
"I don't think that it is serious but in this moment we can't take a risk with Sergio," he said.
"Vinnie was training with the team yesterday but I don't think we can take a risk with Vinnie. Maybe he is ready for the next game against Everton."
With City so many points behind United in the Premier League, the FA Cup might provide a slightly easier chance of silverware for Mancini's men who won the competition in 2011.
"For a team like us it is very important to win something every year," the Italian said.
"It's better if it is Premier League or Champions League, Europa League. But also the FA Cup is important."
He had faint hopes that United's European disappointment might knock their confidence but all his side could really do was try to win every game.
"We hope (it affects their confidence)," he said. "Sometimes it is possible but they are strong enough.
"Our job is only to try to the end of the season ... It is important to be strong in the difficult moments.
"We can improve, we have 10 games (to play in the league) and we need to work for this."