The Reds secured a vital 2-0 Premier League win over the Blues at the weekend, which saw them return to the top of the table by two points ahead of Manchester City.
A Sadio Mane header opened the scoring early in the second half before Salah doubled Liverpool's lead two minutes later with a stunning strike from 25-yards out which flew into the top corner of the net.
The brilliant goal came just three days after a group of Chelsea fans were filmed singing "Salah is a bomber" in a local bar before the club faced Slavia Prague in the Europa League.
The Egyptian is a Muslim and there has been a public outcry of sympathy in reaction to the video, with Chelsea set to issue significant bans to the supporters responsible.
Robertson backed his Liverpool colleague in the aftermath of their latest victory, insisting that his goal was the best possible response to the mindless hate he has received.
“There was a bit of stuff that had gone on in the week and that’s the way to shut them up," he told the Evening Standard.
“The club released a statement on the day and Mo was fine about it. It’s not nice but he dealt with it. It didn’t affect him at all – it didn’t look like it, did it?
“Sadly people are getting used to things like this now because it is happening far too often. Raheem Sterling said the other day that the only way to shut people like this up is to score goals and to beat them (their team). I know it is only a minority of Chelsea fans but Mo certainly quietened them down."
Salah's thunderous strike was his 19th Premier League goal of the 2018-19 campaign, taking him level with City's Sergio Aguero in the race for the Golden Boot.
The 26-year-old has faced plenty of criticism since the turn of the year, having suffered an uncharacteristic goal drought, but his latest effort was a stark reminder of his unique quality.
Robertson hopes Salah's confidence will now be renewed heading into the final weeks of the season, as he added: "It was a fantastic goal. He cut inside and clearly fancied his chances.
"As soon as he hit it, everyone knew that it was in. The place went wild and fair play to him.
“He has come under a bit of criticism (for his performances) this season, unfairly in my opinion. But that will silence them too and hopefully, that will give him a lot of confidence going into the final games.”
The Reds will then turn their attention to Cardiff City on Sunday, as the crucial fixtures begin to pile up in their hunt for silverware.