Jurgen Klopp’s side were looking to return to winning ways in the Champions League following a 1-0 loss to Napoli in Naples last month.
Senegal international Sadio Mane broke the deadlock with a superb goal after the 27-year-old combined with Roberto Firmino at Anfield.
The Liverpool FC full-backs missed out on a place in Uefa’s Best team of the year despite playing a big part in the club’s title success last term.
The duo worked together to make it 2-0 when Alexander-Arnold’s cross picked out Robertson in the penalty area, and the Scottish defender made no mistake with his finish.
Mohamed Salah extended Liverpool FC’s lead to three goals before Salzburg forward Hwang Hee-chan reduced the deficit before half-time.
Hee-chan reduced the deficit to one goal when he netted 11 minutes into the second half before Salzburg substitute Erling Braut Haland levelled in the 60th minute.
However, Salah sealed Liverpool FC’s first win of the Champions League group-stage campaign with his second of the night.
Former Liverpool FC defender Carragher lavished praise on Alexander-Arnold and Robertson for their performances in the Champions League win.
Carragher wrote on Twitter: “Who grows up & wants to be a full back! #robbo #trent @ChampionsLeague”
Liverpool FC will return to Premier League action with a home clash against Leicester City at Anfield on Saturday afternoon.
The Reds are sitting at the top of the Premier League table and five points ahead of second-placed Manchester City.
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