Roberto Mancini has conceded that Joe Hart had a point in saying Manchester City should have been able to hang on to their advantage in the Bernabéu better than they did, accepting that his side made a mistake in defending too deep for the last five minutes.

The City manager did not mention Hart by name, but essentially agreed with the goalkeeper he criticised in the immediate aftermath of the 3-2 defeat by Real Madrid, that a Champions League side good enough to take a 2-1 lead in one of Europe's most intimidating arenas needed to be smart enough to see out the game without conceding twice in the closing seconds.

"In the second half in Madrid we played really well, but it was a mistake to drop back too deep after scoring our second goal," Mancini said. "We conceded a lot of space to players as good as Karim Benzema and Cristiano Ronaldo, and that's what cost us. If we are going to get out of this Champions League group we need to improve very quickly because we only have five games left, and we need to stop conceding easy goals like we did in Madrid."

City play their first home game of the campaign against Borussia Dortmund, facing up to the possibility that another defeat would leave them pointless after two matches and looking at a repeat of last year's scenario, when despite claiming a respectable total of 10 points – enough for Internazionale to top their group and two more than the total that took CSKA Moscow through – they could only manage a third-place finish and a switch to the unloved Europa League.

Part of the reason City struggled last season was because Bayern Munich were so good, topping their group with 13 points and going on to reach the final, yet as Mancini is only too aware, Dortmund's credentials are even stronger. "In my opinion they are one of the best teams in Europe," the City manager said. "They are young, they have good players such as Robert Lewandowski and Marco Reus, and they have finished ahead of Bayern Munich for the past two years. This is going to be another tough game for us, because you cannot win two Bundesliga titles unless you are a strong team. If we concede too much space again, we will pay for it."

In their short Champions League history City have known little other than tough games, yet Mancini feels his side have simply been again unlucky with the draw, rather than victims of a Uefa seeding policy that places a greater importance on qualification consistency rather than recent achievement.

Arsenal were seeded higher than City, for instance, because of their long Champions League history, and consequently found themselves in an easier group, whereas the newly crowned champions of England managed to draw the champions of Spain, Germany and the Netherlands as opponents.

Last season City had to take what was coming, as Champions League debutants who had finished third in the Premier League, but their reward for winning the English title has been to find themselves in an even more challenging group.

"Even if you win your domestic league you still need to be lucky with the draw," Mancini said. "We could have been luckier, we ended up with the best teams in Spain, Germany and Holland, but all Champions League games are difficult. You are bound to be playing against the best teams from other countries, even when they are not the actual champions.

"For that reason, it is a difficult competition. Our aim this season is to improve on last season and at least get out of the group, but in this group, getting to the second stage is not going to be easy.For a second year we are in the toughest group, but we know we are also a strong team and we have to play with confidence."

Jack Rodwell is available for selection if necessary, Maicon and Micah Richards will not be fit in time, and Mancini says he is undecided about whether to bring Joleon Lescott back into the side after preferring Matija Nastasic in Madrid. The Serbian defender kept his place alongside Vincent Kompany for City's last league game, a win at Fulham that Mancini described as an important result ahead of the next big European test.

Yaya Touré, City's outstanding performer in the Bernabéu, also accepts City must improve on their Madrid showing and cut out the mistakes if they are to have any chance of getting through. "We need to improve in difficult situations," the City midfielder said.

"We made mistakes in Madrid and the most important thing is to try not to repeat them. We have tough, tough teams in our group and we must focus on doing our jobs properly. This is only our second Champions League season but we want to improve step by step. We can still do that, but losing in Madrid has left us in need of a good result in our first home game. We want to show our fans we still have a chance of going a long way."