City host Blackburn on Monday night in the Premier League - weather permitting - having won all three matches and conceded no goals since Mancini replaced Mark Hughes as manager at Eastlands last month.
The team lost only twice under Hughes this season and failed to score in just two matches, but through October and November they drew a remarkable seven league fixtures in a row and defeated Sunderland 4-3 in his final game in charge.
So far, Mancini has overseen league victories against Stoke and Wolves and an FA Cup win at Middlesbrough with clean sheets kept in each, and Allardyce believes the Italian will have made the task of tightening his back line an immediate priority.
"I think they are probably a little more defensive," Allardyce said.
"I think he (Mancini) has had a look and thought even though they have only lost two, they have drawn so many games because they haven't managed to keep the clean sheet.
"If they had done that they would have won more games rather than drawn them, where it's the opposite for us - we've not scored enough.
"They have always managed to score with the talent they have got but they have been a little open and lost some very important leads to end up drawing. I think he's put that right."
While City have been fighting it out at the top end of the table for a Champions League place, Blackburn have had an inconsistent first half to the season and currently find themselves just three points away from the relegation zone.
Rovers seem to have overcome their own defensive problems which saw them beaten 6-2 at Arsenal and 5-0 at Chelsea earlier in the campaign, but it is the team's poor goal return which has emerged as a bigger concern.
Allardyce's side are without a league win since November and although he has been generally satisfied with their level of performance, the manager accepts his players must start hitting the back of the net to pull themselves away from trouble.
"It's a big worry because I didn't think it (the bottom half of the league) would be this close from our point of view, based on our performances over the last 20 games," Allardyce said.
"But unfortunately we haven't scored enough goals - there are 10 games this year that we haven't scored in. That shows you our problem really.
"We have not done so bad really, clean sheet-wise - we have got four in the last 10 (league) games having had a particularly poor run in the first 10.
"We seem to have put that right a little bit but not got enough goals to clinch more victories, so instead of winning five in the last 10, we have only won two and drawn five, and that's the massive difference that you then get in the league situation.
"We must put that right. We haven't won in eight and it's very close to being very good, but unfortunately draws are not enough.
"We need to get some wins and we need to get them very quickly.
"That is going to be very difficult at Manchester City but not impossible, so a positive result is what we will look for."
Source: Team Talk
Source: Team Talk