The 27-year-old Swiss international midfielder came off the bench to take his tally to five goals in 13 league appearances, meaning he is already just three shy of his best previous total in the Premier League for Stoke last season.
His double restored Liverpool to the top of the table, one point clear of champions Manchester City.
Shaqiri, who is seeking to prove he is up to playing for a big club having failed at Bayern Munich and Inter Milan, puts his good form down to Liverpool manager Jurgen Klopp’s philosophy in how to play the game.
“Of course the style, how they play, it’s for me too,” he said.
“I have to go on the pitch and perform and I have qualities to be in the team, to have an impact, to decide games.
“I’m very happy at the moment with my performances.
“It was a beautiful feeling to score two goals against Manchester United, an important game against a big rival for Liverpool.”
Shaqiri, who signed for Liverpool in the summer when they triggered a £13.5 million release clause in his contract with relegated Stoke, says being on the bench is not ideal but it only motivates him to prove himself as he did on Sunday.
“For me, I just want to improve, I’m 27, my best age to perform at a high level, so I hope the best times are coming,” said Shaqiri, who spent three seasons at Stoke.
“I’m in a good way and I want to help this club to try to achieve a lot of things and we are in a good way.
“Obviously I’d be lying if I said you are not disappointed when you are on the bench — every player is disappointed when he’s on the bench.
“But I always stay positive and try to help the team when I come on and you saw when I came on I tried to help the team and to have an impact.”
© Agence France-Presse (Additional edits by Michael Corry)