A number of offensive songs were heard from the section of Shielfield Park housing travelling supporters at the Irn-Bru Third Division match, which was broadcast live on ESPN.
Northumbria Police said there had been two arrests over sectarian chants and video footage was being reviewed. Officers said legislation covering sectarian chanting applied to travelling fans and was enactable outside Scotland.
Rangers issued an apology while the match was still ongoing after ESPN microphones picked up the offensive chants. A Rangers spokesman said: "The club is disappointed by certain outbursts of inappropriate singing by a section of the support at Berwick.
"Our fans have been excellent this season both home and away and we do not want to see this tarnished."
Rangers boss Ally McCoist said after the 3-1 success: "I didn't know anything about it until I came in after the game.
"Our supporters have been nothing short of sensational home and away this season. If they were a little bit out of order today, I apologise."
He added: "I think we've all come a long way in recent years - We have to continue the good work that's been done before."
ESPN presenter Ray Stubbs said the broadcaster was contacting the police over the issue.
Rangers TV presenter Andrew Dickson also tweeted during the game, urging fans to "grow up".
He then replied to other Twitter users: "If those who think what was sung in the first half is acceptable, they should look at 99% of the users on Twitter who disagree with them."
Superintendent Tim Smith, of Northumbria Police, confirmed that they had made arrests and were reviewing footage of the match.
He said: "We identified that some chanting had taken place, we've taken video evidence of that to do follow-up inquiries and, in addition to that, two people have been arrested for that offence today."
Smith said video footage would be passed to the Focus (Football Co-ordination Unit for Scotland) team from Strathclyde Police.
However, the force also praised the majority of fans at the game, who it said were "by and large" good-natured.