Five goals at the Etihad Stadium - two each for Alvaro Negredo and Edin Dzeko and one for returning forward Sergio Aguero - meant City moved to the brink of taking their tally into three figures in mid-January.
Pellegrini's men, who face Watford in the fourth round next, have now struck 64 times at home and showed no remorse for their Sky Bet Championship opponents, evident by the fact they brought on the prolific Aguero with the hosts already three goals up.
With City now on course to smash goalscoring records this season, Pellegrini insists his side will continue that pursuit with a relentless nature down the stretch.
"It's an important amount of goals," he said.
"I repeat when I arrived here it was important to try and win a trophy but in the way this team must play and it's important for the fans to come here and know that we are going to try and score the most amount of goals we can."
City could have entered cruise control when Aguero entered the stage with 18 minutes to go, yet the fact he scored within 50 seconds of arriving was typical of their attitude of late.
Pellegrini added: "We continue playing a style of football that is very important. Not to score just one goal and try to keep the ball and not give possession to the other team.
"It's more easy to go backwards with 10 players and try to counter attack with two or three players but it's not my philosophy, it's not the philosophy that this club wants to play.
"We continue to try and play during 90-95 minutes every game, independent of the score we try to be a balanced team, an attractive team."
Negredo surpassed Aguero, who was back after an eight-game absence due to a calf injury, as the club's top scorer this season with the former having struck 21 times to the latter's 20. And with Dzeko also bagging a brace, Pellegrini may have some selection dilemmas to consider.
"For me that's not a problem," he claimed.
"It's a problem when you don't have the players to choose. Alvaro and Edin Dzeko are in a very good moment, it's very important for the team that Sergio comes back today and he scores in this game. We have so many games in the future we have no problem with the three."
The Barclays Premier League side had been due to go to Abu Dhabi this week for some warm weather training before Rovers ground out a credible 1-1 draw at Ewood Park earlier this month to force a replay.
In the lashing Manchester rain, there was little evidence City would have rather been in more tropical climes.
"There are times when you just have to admire quality and they certainly have that," said Rovers boss Gary Bowyer.
"People are talking about them winning all four (trophies) and you can see that happening with the world-class players they have. They were outstandingly clinical today in front of goal."
Pellegrini had suggested the five-goal thrashing was harsh on Blackburn, who at least managed to concede fewer than the likes of Arsenal, Tottenham and West Ham here.
Negredo's opening goal in first-half stoppage time was pinpointed as pivotal by the City boss and the visitors enjoyed good spells of possession before Dzeko swept home a third.
Bowyer had no complaints about the scoreline, though, and was pleased his young side restored some pride after a crisis-ridden 18-months following their top-flight demotion.
"It was 5-0 and it'll be 5-0 in the papers and it's not harsh because the finishing was clinical from them, you have to admire that," the Blackburn boss admitted.
"But I'm nothing but proud of our players for how they have come about and had a go. A lot has been said and written about the mentality of our football club in the last couple of years but they put it back up there with their desire to keep going."