It looks a tough ask for the north Londoners at the Estadio da Luz, where Sherwood will be without 11 first-team players for a last-16 second-leg tie they head into 3-1 down.
Another defeat would heap further pressure on Sherwood, who had to answer yet more questions about his future at the pre-match press conference in Lisbon.
Louis van Gaal is the bookmakers' favourite to take over at the White Hart Lane helm and he recently fuelled speculation by reaffirming his desire to manage in the Premier League.
But Sherwood, who was given an 18-month deal in December, was unmoved by the Netherlands manager's latest comments.
"People ask me this all the time, he is obviously destined to want to manage in England," Sherwood said.
"He has got a good track record, he is a good manager and I'm sure he'll get his opportunity: he's been shouting loud enough for it."
Despite such comments and those questioning his future, Sherwood expects to be in charge at the start of next season and is planning accordingly.
The Spurs boss spoke about the need to alter the club's transfer policy and downplayed reports that a deal is close for Dnipro winger Yevhen Konoplyanka.
"Konoplyanka is certainly one who's being talked about, but nothing definitive," Sherwood said.
"I think we have to make sure we see a lot more of these guys before they come in, not just the highlights, because we've got to make sure we do our recruitment job on them.
"I will sign the players, absolutely
Nobody else will come in here unless I sanction it
You can't work any other way.
"The manager has got to work with the players, so unless he gets the players he wants it's always going to be an uphill task
He will always have the excuse of, 'well, they're not my players'.
"Someone else has made those decisions in the past and I've not been privy to it
I know the type of players I want to improve the group and take it forward next season.
"It's out of my hands but I believe I'll be here next year
I'm planning for next season
The players are playing for their futures."
Source : PA
Source: PA