Dutchman Martin Jol, the man who was left to pick up the pieces after Santini's sudden departure on Friday for "personal reasons", said the players were still in shock, but hinted that he would like the chance to be handed the job.
Jol, brought in by sporting director Frank Arnesen as Santini's right-hand man in the close season, watched as Spurs capitulated to trail 3-0 after 49 minutes before a late rally almost staved off a fourth Premier League defeat in a row.
"After that?" Jol joked, when asked if he would like to take the Tottenham reins.
"The board and (chairman) Daniel Levy are meeting and I will wait and see what Frank says," added Jol, who said one of his ambitions is to manage in the Premier League.
"I think the players were still in shock," said the former West Bromwich Albion player, who won the Dutch Cup as coach of Roda JC Kerkrade in 1997 and also steered unfashionable RKC Waalwijk to promotion.
"To find ourselves 3-0 down was a nightmare, but the team showed great character to come back. It has been very emotional."
Asked if he picked the team, Jol said: "I wrote the names down. But there wasn't really much to change apart from Robbie Keane playing out on the left."
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Spurs forward Freddie Kanoute said Santini's resignation had been a big disappointment to the players, but he believes Jol should be considered.
"He has the respect of all the players, I'm sure he could take the job," said Kanoute, who played under Santini at Olympique Lyon.
"It was a big disappointment for the players when we heard about Mr Santini, we didn't know anything about it until the last minute like everybody else.
"We will never know exactly how (Santini) would have got on here because he had too short a time in charge.
"This has come at a bad time for the club but it's up to the players now. We have to put it right and fight together. I'm sure Martin will do a good job."