Pedersen ended speculation about his future on Wednesday by signing a new four-year-deal with Rovers, who he joined from Tromso in 2004.
In the six years since then the winger has taken part in two European campaigns with the Lancashire club - in the UEFA Cup in 2006/07 and 2007/08 - and Pedersen feels Allardyce is capable of taking Blackburn back to that level in the near future.
"Our manager is one of the top managers in Britain. I'm confident that he will build a team that can be competitive in the Premier League," Pedersen told the Lancashire Telegraph.
"Anything can happen. Fulham was the perfect example of that when reaching the final in the Europa League this season.
"I am confident our manager will bring us up to the level where we can compete for a spot in the Europa League.
"Liverpool, Chelsea, Manchester United, Arsenal may be the big four clubs but Manchester City, Tottenham, Aston Villa and Everton are all challengers for a Champions League spot. This shows the strength of Premier League football."
Pedersen's previous deal ran out this summer and he had been linked with a number of clubs from around Europe.
But the Norway international opted to extend his stay at Ewood Park and is now looking forward to a bright future with Blackburn.
"I feel devoted to Blackburn and the team," Pedersen said.
"I've been with Blackburn for six years now, during that time I've experienced ups and downs, high and lows but I've always felt appreciated and the club has great supporters.
"Those are factors that I value highly and they make me want to go that extra mile.
"Looking forward, Blackburn will have an interesting mix of young talent and experienced players this upcoming season.
"I want to be a part of that. I'm also hoping for a chance at Europe again."
There had been some doubt as to whether Pedersen would re-commit to Rovers, but the 28-year-old insists he always hoped to stay.
"There's been a lot of speculation about me going elsewhere but Blackburn always was my first choice," he said.
"It's been a time-consuming process for both parties but there was never any drama or hard feelings involved.
"We've always been on good terms, it just has taken a little longer than expected.
"I'm pleased and very proud to re-sign with Blackburn and I look forward to another four years and new challenges with the club."
Source: Team Talk
Source: Team Talk