After the game, Vertonghen insisted he was fine despite having to be helped off the pitch but Pochettino admitted Spurs would continue to monitor the defender for signs of concussion.
Asked whether he was comfortable with the decision to allow Vertonghen to return to the pitch, Pochettino said: "I wasn't involved. That was the doctor's decision. The rules and protocol are so important, and our medical staff followed the protocol. Now he's OK, he walked away, I hope he is OK, but you know very well that we need to keep an eye on him.
"We must protect the players, of course. I was out of the conversation, our medical staff followed the protocol and they decided he could continue the game, but then he started feeling unwell and he had to come off."
Vertonghen suffered a horrible-looking knock in the first half after challenging for a high ball and accidentally clashing heads with teammate Toby Alderweireld.
Players from both sides expressed concern and frantically waved Tottenham's medical staff onto the pitch as the Belgian defender lay on the turf. He received treatment for several minutes, blood pouring from his nose, and initially seemed OK to continue and able to walk around the edge of the pitch with no aid.
The Spurs physiotherapists assessed Vertonghen and decided he could re-enter the field of play, but almost immediately his knees buckled and had to be helped down the tunnel by two members of the Tottenham backroom staff, appearing to be in some distress.
However, after the game Vertonghen insisted that he was fine while walking through the mixed zone and telling journalists he had suffered no concussion and no broken bones, with only a small patch on his nose.
Pochettino was asked if the sight of the defender virtually collapsing on the touchline affected him or his decision-making.
"In this moment you are focused on the game, it's difficult to think too much," he said. "You must liaise with the medical staff. The most important thing is the health of the player.
"I wasn't involved [in the decision] and I don't want to be involved in the future. If they said 'change' [substitute the player], I'm not going to doubt them. I will listen and will never question the decision of the medical staff.
"For me, first of all it's your life. We must protect the player and of course I was out of the conversation and our medical [staff] followed the protocol and decided it was possible to restart the game and it's time to play again.
"But of course it was Jan in that moment and the following action that he started to feel unwell and we check him with the doctor."
The club released a statement on Wednesday, updating Vertonghen's status, saying: "Jan Vertonghen has undergone further assessment today [Wednesday 1 May] after sustaining a head injury in last night's Champions League semi-final first leg against Ajax. 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."
Brain injury charity Headway have suggested temporary concussion substitutions as one way to ensure "longer off-pitch assessments are conducted" and said "the pressure on club medical staff is enormous and unfair, particularly in such high-stakes games such as a Champions League semifinal."
FIFPro echoed that and pointed to NFL procedures "where a player can be taken out for 10 or 15 minutes, you can take time to make a decision." The European players' union also called for independent doctors to be used rather than club specific medical staff and called for changes to be implemented in time for the Women's World Cup this summer.
The Spurs' boss was not pleased with his team's performance overall -- with a Donny van de Beek goal leaving his team with plenty of work to do next Wednesday in Amsterdam -- but took full responsibility for the performance.
"The attitude was there, but we didn't find a way to play," said Pochettino. "We didn't show the energy that we wanted to show. They showed more energy than us. The way we conceded the goal was painful. They were more proactive than us.
"Our approach to the game was not good. I am the manager so I have responsibility."
