The row dominated the build-up to the draw between Queens Park Rangers and Chelsea, and mirrored recent incidents.
Taylor told BBC Radio 5 live: “We have to move on. These things will separate us and become like some mafia feud.”
The 67-year-old also insisted pre-match handshakes should remain.
The goodwill gesture before kick-off between opposing players was brought into the Premier League in 2008-09 as a part of the ‘Get on with the Game’ initiative.
“Owners, managers, chief executives and players said ‘yes’ [to the idea] and I do not know why we should say ‘no’ now,” Taylor added.
“They are not betraying any personal principles. It is being done for the image of the game and to set the right example to the mascots and youngsters playing at school.”
Following its introduction, a number of high-profile flashpoints have occurred.
In February 2010, Manchester City left-back Wayne Bridge refused the hand of former England and Chelsea team-mate Terry following allegations of an affair between Bridge’s ex-girlfriend and Terry.
Two years later, Liverpool striker Luis Suarez turned away from Patrice Evra before the league clash between Manchester United and Liverpool. This followed the Uruguay striker serving an eight-match ban for racially abusing the France left-back in a previous encounter.
There has been no request for handshakes to be cancelled when the rivals meet at Anfield on Sunday.
Terry was accused of racially abusing Ferdinand during a Premier League match last October. The Chelsea man was cleared in court but faces an FA charge later this month.
Handshakes were abandoned in the return league game last season between the west London clubs, as well as before their FA Cup meeting.
Speaking on Match of the Day 2, former England striker Dion Dublin said he believed the football authorities should “do away” with enforced handshakes.
He said: “It has been forced on the two players [Ferdinand and Terry]. I think it is wrong.
“Do away with the handshake. If you have play against an opponent, after the game shake their hand. Leave them to deal with the situation themselves.”