City have won only two of their five Premier League matches this season and have yet to keep a clean sheet.
"What we did [last season] is finished. It is in the past, it is history," Mancini said.
"Now we are like all the other teams. And I don't like that we have had three draws, like today, probably we are missing two points against Stoke maybe. But we need to work because we want to improve this."
Wenger credits Arsenal 'spirit'
Mancini's exasperation was evident at the final whistle as he appeared to push Mario Balotelli down the tunnel after the pair exchanged words on the touchline.
The Italian striker was disappointed to be left out of the squad for the Champions League match with Real Madrid and only came on for the last five minutes of Sunday's match against Arsenal.
After the match Mancini attempted to play down the incident. When asked if he pushed Balotelli, Mancini said: "I don't remember. I don't remember. It's possible but I don't remember what happened after the game.
"I don't know if he asked me something. Maybe. It is not important. Mario thinks it was important probably."
City were second best for much of the first half at the Etihad but snatched the lead against the run of play when Joleon Lescott headed in David Silva's corner five minutes before half-time.
Arsenal equalised with nine minutes remaining when Laurent Koscielny thumped in from close range after City had failed to clear a corner.
City might have stretched their lead during the second half as Sergio Aguero and Yaya Toure went close. But their failure to take those opportunities was at the heart of Mancini's disappointment.
"This year we have one problem, we don't close the game and don't score more goals," Mancini added.
"We had three or four chances in the second half and didn't score. I am frustrated about the result, because we had a chance to win and we conceded another goal. We need to work harder.
Despite the draw, Manchester City extended their unbeaten home league run to 32 matches, stretching back to a 2-1 loss at Everton in December 2010.
"I am sure Arsenal will fight for the title this year because they have a good team, but it is going to be difficult for everyone, especially with playing in the Champions League."
Arsenal manager Arsene Wenger felt a point was the least his side's performance warranted and said he believed they might have come away with all three had the Gunners been more clinical in front of goal.
"I am pleased, because I feel a point was the minimum we deserved today," he said.
"I am pleased with the quality of our performance and our spirit. But I am a bit frustrated because I felt there was room to do more.
"We had early chances and of course very late chances, especially the chance for Gervinho on the edge of the box, where we missed the target.
"But overall I hope the game will reinforce our belief and our confidence and reassure us about our potential in this league."
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