The Swiss outfit were unlucky to leave the Stade Gerland on the back of a 1-0 first-leg defeat as a resolute defensive display - in front of an in-form Burki - was undone by Milan Bisevac's second-half header.
However, 22-year-old Burki feels Grasshoppers are well-placed to overturn the slender deficit in Zurich.
He told UEFA.com: "We hit the woodwork twice and had other big chances. We couldn't have done much more and can be happy with our performance.
"We're on a level playing field with Lyon and there is a real possibility for us to progress in the second leg."
Despite a fierce domestic rivalry between the two clubs in the Swiss Super League, Burki is happy to use the good example set by champions Basle, who reached the last four of the Europa League last season.
"Basle made it to the semi-finals of the Europa League and have beaten Manchester United when nobody gave them a chance," Burki added. "We want to make the impossible possible."
Basle, meanwhile, take their own 1-0 lead to Maccabi Tel-Aviv thanks to Valentin Stocker's first-leg goal.
Fenerbahce started the summer with a two-year suspension from European competition for alleged involvement in match-fixing but, after the ban was suspended by the Court of Arbitration for Sport, the Istanbul giants claimed a 1-1 draw at Red Bull Salzburg to gain a slight advantage over their Austrian opponents.
Roger Schmidt's Salzburg now have to score at the Sukru Saracoglu to stand any chance of reaching the play-off round, where clubs including AC Milan, Arsenal and Schalke await.
Partizan Belgrade coach Vuk Rasovic hopes his players can stamp out their recent indiscipline to overcome a 2-1 deficit and progress beyond Bulgarian side Ludogorets.
The Serbian club lost Vladimir Voltov to a red card while squeezing past Shirak in the second round and Milos Jojic will miss tomorrow's game after receiving his marching orders in Razgrad last week.
"Our players lack experience and that might be some explanation for their behaviour on the pitch and the number of cards, yellow and red, they have received," Rasovic told UEFA.com.
"Both red cards have come for second bookable offences - for fouls which are not that serious but which you have to avoid at this level. We have to learn and I hope those mistakes will not be repeated."
Elsewhere, Kazakh champions Shakhtyor Karagandy take a dominant 3-0 lead to Skenderbeu of Albania while Steaua Bucharest look to preserve a 2-0 advantage when Georgia's Dinamo Tbilisi arrive in the Romanian capital.
Apoel Nicosia must score in Portugal to progress after Maribor claimed a 1-1 draw in Cyprus.