Sergio Aguero's second-half strike was the difference in a chaotic clash at the Etihad Stadium, with the visitors reduced to 10 men for the majority after Chris Smalling picked up a second yellow card.
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"We responded well and defended well [after conceding]," Rooney told MUTV. "I felt for long periods of the game we were the better team. We took control of the game with 10 men and created the better chances.
"We were unfortunate not to get anything out of the match and we're disappointed to leave with no points after a great effort.
"Chris is disappointed. It's tough when you get sent off, especially in a derby and with such a long time to go in the game it made it difficult for the rest of us to hold on. I'm sure Chris will learn from that."
The result leaves United 13 points behind league-leaders Chelsea with 10 games played, but Rooney is confident Louis van Gaal's measures are starting to take effect.
Rooney continued: "We're working on different things, which a lot of us haven't been used to. We're certainly heading in the right direction.
"We're progressing each week and playing some nice football. We need to turn that into results and I'm sure we can do that if we keep working, keep learning and keep doing what the manager wants from us."