Frenchman Evra has accused Suarez of racially abusing him over ten times during the meeting between their respective sides on Saturday afternoon.
The FA have confirmed that they are investigating those allegations, a decision which Taylor has backed.
"It is very unfortunate we've got two of our foreign players involved here in a high-profile match in a high-profile dispute of the most sensitive nature," Taylor told Sky Sports News.
"It is important that there is a full enquiry to try and get to the bottom of it.
"It is also important to make sure that if something did happen, it doesn't happen again."
The match at Anfield ended 1-1.