The Premier League champions were outplayed for much of their clash with the German outfit, who have won two consecutive Bundesliga titles, but managed to save a point after Mario Balotelli's late penalty cancelled out Marco Reus' well taken opener.
City were eliminated in the group stages of the last season's competition, and appear in danger of suffering the same fate this term after taking just a solitary point from their first two games.
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He told Sky Sports: "We didn’t play well because Borussia Dortmund played better than us. I think probably in this moment they are a better team than us. If we want to play at the top level in the Champions League, we need to run more than tonight.
"We need to run, fight for every ball. It is not enough to have a good pass sometimes in the Champions League. The Champions League is another situation, totally different from the championship, for every team. And we need to fight. We need to run. It is not enough to have just a good quality."
However, the former Inter manager insisted he was not surprised that his side found it difficult against a side of Dortmund's quality.
"I knew before the game that it is difficult because Borussia Dortmund used to play Champions League every year, is more experienced than us," he added.
"But we have good players, we can play like they did this evening."