Mancini was unable to select injured trio David Silva, Mario Balotelli and Aleksandar Kolarov and he said it was not realistic to expect City to win every game they play, especially away from Eastlands.
"Before the game we believed we could win it, but today we were missing three important players away from home," said the Italian, whose team did not produce a single shot on target in the 90 minutes.
"It's impossible for us to win every game we play. Arsenal played some good football but after the first 15 minutes they were mostly taking shots from distance, so that shows we defended well.
"I like to play football better than we did on this occasion, but it is important to remember that we have played four games in 10 days and it was a tough night.
"If you can't win, don't lose, and we didn't."
Arsenal boss Arsene Wenger admitted the draw left him frustrated as the Gunners also missed an opportunity to increase the pressure on United at the top.
Wenger proud of Arsenal display
"Of course it was frustrating, but I'm proud of the players collectively and individually," said Wenger. "It isn't easy when you face a team who are set up not to concede a goal.
"When you don't score you always feel like you could have done more to get one, but I feel this is much more of a positive 0-0 than a negative one.
"We looked like we could combine quickly to score, but when we got tired it became more difficult. We faced 80% of the game playing against 10 men in the final third and that's not easy.
"I respect the way City played, because it is up to us to score the first goal and it didn't happen. Whatever problem you have you must solve it, but the way they set up is definitely a compliment to my team."
Mancini and Wenger agreed that Bacary Sagna and Pablo Zabaleta were unlucky to receive red cards in the last minute after a skirmish on the touchline, despite Sagna appearing to lean his head into the Argentine.
"For me, a yellow card was enough for both players," said Mancini. "Zabaleta will be missing through suspension now, but he didn't do anything wrong."
Wenger added: "I thought we would see two yellows. It was a bit difficult to see, but it looked a bit harsh."
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