Morten Gamst Pedersen netted in either half at Ewood Park to make it three wins for Rovers in their last four Barclays Premier League games. Blackburn were in the relegation zone at the start of the month but are now up to 11th - a position Allardyce thinks more accurately reflects the way they have been playing.
He said: "It's nine points from the last four games, we are into phase two of our season as we look at it and we have already picked up the same amount of points that we picked up in the entire 10 games of phase one. We are well on the way to improving our position in the league and pushing on in phase two."
He added: "This is a very important victory to maintain that progress up the table.
"I think we have played as good as this on many occasions during the first 10 games - Chelsea at Ewood Park for instance, or Birmingham away (both 2-1 defeats) where we didn't get anything.
"Now we are turning performances into results, which is the key thing playing in the Premier League."
Rovers were in action for the first time since being taken over by Indian company Venky's and were watched by Venkateshwara and Balaji Rao, the poultry giant's directors, who came on to the pitch to greet the home supporters before kick-off.
Prior to their £23million takeover being completed on Friday the Venky's hierarchy had witnessed the team's loss against Chelsea and a 4-2 defeat at Tottenham, and Allardyce was pleased now the purchase had been finalised that his players could make it a winning start to the new era.
"I've met the new owners for the third time, only briefly," Allardyce said. "Hopefully, like every Blackburn fan, the players and myself, they will be very happy with the way we have won and the performance that was given.
"I hope the next time we get to meet, which I am looking forward to, we can plan the way forward from here on in."
Source: PA
Source: PA