Gareth Bale's hopes of a long-term future at Spurs appeared to take another negative turn after Jose Mourinho dismissed his injury worries.
Spurs took their hosts to extra time in a wonderfully chaotic game, eventually falling 5-4 to Bernard's 97th-minute winner.
Davinson Sanchez gave the visitors a third minute lead a Goodison Park and completed an unlikely brace to make it 3-3 before the hour - Erik Lamela having reduced the arrears after Dominic Calvert-Lewin, Richarlison and Gylfi Sigurdsson were all on target during a crazy seven-and-a-half-minute spell.
Harry Kane came off the bench to net Tottenham's second equaliser, Richarlison having brilliantly doubled his tally, although Bale was not among the options on the bench to bolster Mourinho's attempts to save the game.
"I think it’s better for me to say," he said at a post-match news conference when asked to explain the Wales star's absence.
"So, we played against West Bromwich on the Sunday and he didn't play. On Monday, I was a bit surprised by him wanting to have a scan because he was not comfortable with some muscular area.
"So, he didn’t train on Monday and then on Tuesday he trained with the team but I was informed that his desire was to work with the sports scientists for a couple of days to strengthen that area. That's the reason why he’s not here.
"I don’t think it’s an obvious, clear injury. I would say he feels uncomfortable. Because of that he could not be 100 per cent, but I don’t think an injury."
Asked to elaborate further on whether Bale had disappointed him, Mourinho replied: "This is Everton post-match and Gareth was not here. The only thing I can say is I am being completely open and honest."
The incident marks another unhelpful chapter in Bale's as-yet deeply underwhelming return to Spurs on loan from Real Madrid, with the chances of a permanent switch back to north London looking increasingly remote.
A scorer in two of his four UEFA Champions League final successes at Madrid, fitness problems dogged Bale over recent seasons as he fell out of favour with Zinedine Zidane.
The 31-year-old has four goals in 16 appearances for Spurs this term, although only two of his six Premier League outings have been starts.
Matters at the other end of the pitch look to be a more immediate concern for Mourinho ahead of Saturday's trip to face in-form Premier League leaders Manchester City.
"I enjoyed the way we played when we had the ball from the first minute," he told BT Sport after the breathless affair on Merseyside. "We had a great dynamic, great movement and great character to fight against incredible mistakes.
"But attacking football only wins matches when you don't make more mistakes than what you create.
"We scored four goals and four goals was not enough.
"It was the mouse and the cat. The mouse was our defensive mistakes and the cat was trying to compensate for that and playing very well."
Spurs must now lick their wounds after a punishing encounter, having seen City rotate their XI and saunter to a 3-1 win in their own last-16 tie at Swansea City earlier on Wednesday.
"Of course, City are great team, they rested a big percentage of their team," Mourinho added. "We have this situation but you can't cry."