Mauricio Pochettino’s side have improved under his stewardship although Spurs are yet to win a trophy under the former Southampton coach.
Tottenham were close to winning the Premier League title two years ago but Leicester City eventually pipped them to the crown.
They were beaten once again in the race for the title last season by Chelsea while Pochettino’s men have also struggled in Europe.
Two years ago they were dumped out of the Europa League by Borussia Dortmund in the last 16 while they did not make it out of the group stages of the Champions League last year.
After dropping into the Europa League, they were knocked out by Ghent in the last 32 and Lloris has now demanded more from his team in Europe.
He told reporters: “It’s been five seasons now that I’m with Spurs and I’ve got a little bit frustrated about Europe.
“We’ve got the talent to go further than we’ve done. Hopefully this season we can prove our real value against the best teams in Europe and go as far as possible.”