Despite being initially cleared to make a return to action, the 32-year-old was forced to come off moments later and had to be helped from the field after struggling to exit the pitch on his own.
Brain injury charity Headway called on Wednesday for a change to the rules of the game relating to protocol, saying that the incident showed the need for "temporary concussion substitutions".
Mauricio Pochettino had already defended the club’s doctors and now Tottenham have issued a further statement clarifying their procedures while revealing that Vertonghen reported no further problems.
"Jan Vertonghen has undergone further assessment today after sustaining a head injury in last night's Champions League semi-final first leg against Ajax," it read .
"He also suffered a small cut to his nose that was bleeding heavily.
"The Belgium defender was assessed on the pitch yesterday immediately after the incident with our medical team strictly following Football Association concussion guidelines.
"Following testing he was judged to be alert and answered all questions correctly and lucidly, deeming him fit to return to the field of play.
"All available video footage was relayed to our on-pitch medical team and they were able to confirm that he had suffered no loss of consciousness.
"Jan was immediately withdrawn as a result of the player informing medical staff that symptoms were developing suddenly and that he no longer felt stable standing up.
"Tests today have been clear and testing will continue for the next few days. Additionally, as is standard club policy with certain injuries, we shall also be seeking independent advice and Jan is due to see a neurologist, who specialises in elite athletes, tomorrow. The player has reported no ill-effects today."
After the statement was released, former Ajax defender Vertonghen also wrote a message on his Twitter account that said: "Not the way I wanted the game to go last night. Feeling ok today. Thanks to both sets of fans for the positive messages."