Salah was instrumental in Liverpool's equalising goal, taking control of a loose ball, working his way into the box and firing off a shot at goalkeeper Bernd Leno.
The German made the save but Sadio Mane was first to react to the rebound and turned it home to put the Reds back on level terms after Alexandre Lacazette had capitalised on an Andy Robertson error to give the Gunners the lead.
Robertson later made amends for his error, giving Liverpool the lead before the end of the first-half, before new signing Diogo Jota wrapped up all three points with a goal on debut to earn them a 3-1 win.
Analysing the game at half-time, Keane and Carragher looked at Liverpool's equaliser and the problems Salah had caused for Tierney.
"Like any good team, Liverpool responded very quickly," Keane said. "Salah has been causing nightmares for Tierney and it's the least they deserved [the equaliser].
"The keeper should probably do better with the initial shot. Tierney had to keep him on the outside and then Leno has to do better."
Carragher added: "Tierney can't cope with Salah on this left side and the second goal again comes from that. Maitland-Niles is getting high up the pitch so Tierney is often found in the full-back area.
"The delivery from Trent Alexander-Arnold has been fantastic and Robertson makes up for his mistake at the other end.
"There's a problem on that left side for Arsenal that they need to sort out."
Get the latest transfer news straight into your inbox!
Want to be on the ball with all of the latest football news?
Well then sign up for the brilliant new Daily Star Sport email newsletter!
From the latest transfer news to the agenda-setting stories, get it all in your email inbox.
How do you sign up?
It only takes a matter of seconds.
Simply type your email address into the box at the top of this article and hit 'subscribe'.
And that's it, job done. You'll receive an email with all of the top news stories every single morning.
You can find out more information on our email newsletter on this link here.
Tierney was also involved in an incident with Mane in the first-half where the Senegalese forward caught him in the face with his arm.
Mane was attempting to shield the ball from the Scotland international but elbowed him in the process, which could have seen him given a straight red card.
However, referee Craig Pawson opted for a yellow instead.