The French goalkeeper suffered the injury in a collision with Toffees striker Romelu Lukaku, and required a substantial amount of medical attention before groggily returning to his feet.
At one stage it appeared that Lloris was about to leave the Goodison Park pitch, to be replaced by Brad Friedel, before the Tottenham bench opted to keep their first-choice keeper between the sticks.
This led to criticism from FIFA's chief medical officer Professor Jiri Dvorak, as well as the international players' union FIFPro.
And now Taylor has weighed in with his complaints, saying: "I watched the incident on television and I was surprised, to say the least, that he was allowed to stay on.
"We are very concerned that the protocol that involves concussed players was not adhered to and I have raised this at the meeting with the professional game's stakeholders and the decision was taken to remind all clubs of the protocol.
"Managers should not take these decisions in the heat of the moment and that needs reinforcing."
In a statement released by Spurs, the club's head of medical services Wayne Diesel said he was happy for the France captain to carry on.
He said: "Once the relevant tests and assessments were carried out, we were totally satisfied that he was fit to continue playing."