The former Arsenal striker won over the Tottenham fans last year, topping the club's scoring charts with a return of 18 goals in 37 matches while on loan from Manchester City.
But the goals have dried up since Adebayor completed a permanent move last summer and he has scored just three in 24 games this term.
Jermain Defoe's absence with an ankle injury means Adebayor will start the last-32 second leg tie at Stade de Gerland, with Tottenham leading 2-1, and Villas-Boas has backed him to end his barren spell.
"He can still be the player we saw last season," said the Portuguese.
"We're trying to unlock the best out of the player. Last year shows as an example for what we're trying to get out of him.
"Strikers live off goals and we're doing everything we can to try and unlock his full potential."
Adebayor is no stranger to criticism as he also endured difficult spells at Arsenal and City, but Villas-Boas feels he pays little attention to the doubters.
"I'm not sure if it bothers him," he said.
"Players build their own motivations. Perceptions and media opinions can influence the public in general, but I think the player strives on his own motivation in the end.
"I think (he's working as hard).
"The injuries he had and the African Nations Cup took him out for lots of games and Defoe's form this year had been magnificent."
Though Spurs' primary objective is to get back in to the Champions League, it does not mean the club will shy away in their attempts to win the Europa League.
Villas-Boas lifted the trophy in 2011 with Porto before embarking on an ill-fated stint at Chelsea which lasted 256 days and he now wants to win the trophy again to help ease the pain of his short-lived reign at Stamford Bridge.
"After the disappointments I went through last year it would be great to grab the chance of a European trophy," he said. "We won the Europa League with Porto. Both are top clubs."
Gareth Bale's two stunning free-kicks in last week's 2-1 win against Ligue 1's second-placed side mean a 0-0 draw at the Stade de Gerland will see Spurs through to the last 16, where they are likely to meet Inter Milan.
The Spurs boss confirmed that, as was the case in the first leg, Brad Friedel will start in goal ahead of former Lyon captain Hugo Lloris, saying: "We've decided to keep this rotation policy."
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