The match in Krusevac last month ended in chaotic scenes with Danny Rose sent off after kicking the ball away in reaction to the abuse he was receiving.
The Serbian FA later blamed Rose and accused him of "inappropriate, unsportsmanlike and vulgar" behaviour, while calls have been made in England for them to be banned or at least harshly penalised at a hearing that will take place on Thursday.
Taylor said: "If the Serbian FA are found guilty then we would want UEFA to take the strongest possible action.
"Everybody was shocked by the racist chanting at that match and there needs to be a deterrent.
"We have had our own issues in dealing with incidents of racism of course, such as the length of time taken to deal with the John Terry case, but I don't believe it is a case of people in glass houses shouldn't throw stones.
"I believe the FA have grasped the nettle and are trying to bring in improvements."
The racism charge was discussed by FA chairman David Bernstein and sports minister Hugh Robertson at a meeting with UEFA president Michel Platini in Switzerland on Tuesday.
Bernstein told reporters: "I think UEFA understand our position and that there is a degree of sympathy from Platini but I don't want to say anything more than that."