Liverpool fans booed and jeered Evra all match during the FA Cup win over Manchester United, apparently in response to the French defender making a complaint that he was racially abused by Luis Suarez - which led to the Uruguay striker receiving an eight-match ban.
Liverpool boss Kenny Dalglish said there was nothing wrong with the booing and that it was "a bit of banter" but Taylor, chief executive of the Professional Footballers' Association (PFA) is concerned it could have more serious repercussions.
Taylor told Press Association Sport: "The booing of Evra was unwelcome. For someone to be booed for reporting racist comments is not something we want to see happening.
"Black players may be worried about reporting such things if there is going to be a backlash like this."
Taylor said the Suarez ban shows that racism in football is still an issue to be dealt with.
"The game must do all it can to eradicate it," he added.
Meanwhile, FIFA member Prince Ali Bin Al Hussein has said racism cases have done "a lot of damage" to English football.
Prince Ali told www.insideworldfootball.biz: "Obviously it's a huge concern for everyone across the world.
"England has a great track record in terms of fair play and a lot of damage has been done.
"The Premier League is seen all over the world and whatever happens there is picked up everywhere else."
Prince Ali, from Jordan, added that the way in which the Football Association and other football authorities had reacted to the issue had been admired across the world.
He added: "Because of the stature of the Premier League, when people see how things like this are tackled, they reflect on themselves.
"What's important is the solution, not simply focussing on the problem.
"It's a big responsibility. Everyone was watching to see how things would be handled."