A 2-1 victory in Sunday's north-London derby over rivals Arsenal moved Andre Villas-Boas' men back into third in the Barclays Premier League with 10 games to go.
Spurs host Italian giants Inter Milan in the last 16 of the Europa League on Thursday night, a competition their Portuguese coach has won before.
France captain Lloris sees no reason why Spurs cannot continue to strive for success on all fronts.
He said: "Of course there is the Premier League, but also the Europa League, we can do something and why not win a trophy for the club?
"It would be a great thing for this season, but also for the future."