Despite investing millions in the summer, City are struggling to make an impact and have collected only one win in four league games.
A club who view the Champions League arena as the next step are already seven points behind leaders Chelsea.
The teams are due to meet at Eastlands a week on Saturday - one of a number of crucial games, according to Mancini.
City also face Wigan and Newcastle in the league as well as Salzburg on Thursday in the Europa League, then Juventus.
In addition they have a Carling Cup tie against West Brom to contend with before the international break in October.
That is why Mancini is anxious to get some of his players out of the treatment room and onto the training ground as soon as possible. Wayne Bridge, Jerome Boateng, Aleksandar Kolarov and Mario Balotelli all sat out the draw against Rovers at Eastlands on Saturday.
So too did Nigel De Jong (dead leg) and Emmanuel Adebayor (hamstring) because of injuries - but both could travel to Salzburg.
Mancini said: "De Jong was injured on Friday with the very last kick of training. Adebayor's injury came a week ago but I think they should be okay for the next game.
"We have a difficult month until the next international break, we need to get some of our injured players back and win these next six games."
City were hoping to bounce back against Blackburn after the defeat by Sunderland in their last outing but went behind in the 24th minute.
Goalkeeper Joe Hart, now widely recognised as England's number one, and Kolo Toure failed to communicate as Morten Gamst Pedersen launched the ball forward.
It meant Nikola Kalinic was left with an open goal and he took full advantage to open the scoring.
City's pressure paid off when Patrick Vieira equalised in the 55th minute after a neat one-two with Carlos Tevez.
But despite carving out numerous chances Blackburn held firm thanks to Paul Robinson between the posts and Christopher Samba in front of him.
Mancini said: "We were a bit unlucky against Blackburn but we gave them a gift for the opening goal so we will just have to work harder to get through this.
"It was a strange goal. It can happen. This is football. Joe Hart is a good goalkeeper.
"At the moment the luck is against us, but we know we are a good team so we have to keep working well."
However that blunder could offer Republic of Ireland goalkeeper Shay Given a glimmer of hope ahead of the match against Salzburg after he suddenly found himself demoted.
Meanwhile Blackburn boss Sam Allardyce will monitor the fitness of Ryan Nelsen (foot) and Michel Salgado (thigh) after they came off injured in the first half.
Allardyce believes his side can get a lift from the performance against City when Fulham visit Ewood Park on Saturday.
He said: "It was great to get a result like this and hopefully it will boost the players confidence.
"I am glad to say I have not lost my record of losing more than two Premier League games on the trot.
"Now we can look forward to facing Fulham at Ewood Park on Saturday and trying to get three points."