The forward joined Jurgen Klopp's side for £13 million ($17m) following Stoke City's relegation from the Premier League last season and has shown himself an able back-up in attack.
The 27-year-old has scored six times in 20 appearances in the top flight, including a match-winning double against Manchester United in December in a 3-1 win that ultimately cost Jose Mourinho his job as manager.
Shaqiri is likely to be on the bench on Tuesday when Liverpool host his former club Bayern Munich in the first leg of their Champions League last-16 tie.
Nonetheless, Barnetta - who was an international team-mate of Shaqiri's until his retirement in 2014 - thinks he has already shown Jurgen Klopp was right to sign him.
"When I played with him, he was a young player and he's made a lot of steps forward," Barnetta told Omnisport. "He had some tough times when he was not playing that much in Munich and for Inter.
"That's why I'm very happy for him that he went to Liverpool and, when he got his chances, he took them.
"Maybe a lot of people from the outside said, 'What is he doing at Liverpool after Stoke?' but he didn't react to these guys and made some amazing games. Now, I think everyone is quiet on the outside."
Barnetta thinks working under Klopp has proved important to Shaqiri's development, particularly the patience he showed in introducing the player into the first team.
"He [Klopp] is a really good motivator and he really lives football and that's why I think he can take the last per cent out of a player," said the former Bayer Leverkusen winger, now at St Gallen in Switzerland.
"I think that was something Xherdan needed because, like I said, his talent was always there but maybe sometimes he couldn't bring it on the pitch. In the last few months he showed really what he is able to do.
"It's always so important that you have a coach who helps you, who gives you a lot of confidence. It was also important that he didn't bring him in from the beginning. He came from the bench and had a couple of minutes.
"That is why a lot of people were asking, 'What is he doing there?' but it was very well done from the coach to give him the chance to improve and to see how it works, because Anfield is special – it's not like every other team or set of fans.
"That's why I think Jurgen Klopp has a lot of profit from this success from Xherdan."