The Portugal international sustained a potentially season-ending injury after being clipped by Son Heung-min and falling heavily on his right leg, resulting in a fracture dislocation to his right ankle for which he will undergo surgery on Monday.
Tosun, who had only been on the pitch for 10 minutes, comforted the midfielder as many players around them were visibly shaken by the severity of the injury.
Son, who was initially shown a yellow card by referee Martin Atkinson before it was changed to a red, was in tears but incredibly Tosun picked himself up to score a header eight minutes into 12 added on to cancel out Dele Alli's first away league goal since January.
"Everybody is sad inside. Some players, they nearly cried," said the Turkey international. "He was in shock, his eyes were open so big. He was like crying, shouting and screaming.
"I just tried to hold him and speak to him. I tried to tell him to stay calm. We couldn't understand him."
Tottenham are considering an appeal against the red card shown to Son, who slid in and clipped his opponent but not recklessly so.
The Premier League issued a statement after the game to clarify why the card had been upgraded, in which it said: "The red card for Son was for endangering the safety of a player which happened as a consequence of his initial challenge."
However, Tottenham manager Mauricio Pochettino felt the injury led to an over-reaction which resulted in a greater punishment for Son.
"It was clear it was never the intention of Son to create the problem that happened afterwards. It is unbelievable to see a red card," said the Spurs boss.
"In that situation we need to help because the decision of the referee was a yellow card but the VAR changed the decision. It is the latest example of it being not clear.
"VAR needs to check if it was a bad tackle from Son and judge the action, not what happened after.
"We all feel sorry for Andre. I want to send my best wishes to him and to his family in this tough moment. We want to send, on behalf of the squad, our best wishes.
"I don't know what will happen now (in terms of an appeal). The club will see if it is possible but what we cannot change is what happened after (the incident)."
Pochettino did, however, praise Everton's players for their reaction and their support for the distraught Son - particularly club captain Seamus Coleman, who was out for a year after suffering a similarly-horrific double-fracture of his lower leg in March 2017.
"The players from Everton were fantastic. The captain came to the dressing room to console Son," said the Argentinian. "I want to say thank you to the players and Coleman, who came in on behalf of the squad of Everton."