The France international arrived at White Hart Lane on transfer deadline day but witnessed the American shot-stopper give a man of the match performance against Norwich just a day later.
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And, though manager Andre Villas-Boas kept faith in the 41-year-old yet again on Sunday, Lloris revealed he is "expecting" to make his debut soon.
"Things were very clear from the start on Sunday," Lloris told L'Equipe. "I was at Tony Parks' (Tottenham's goalkeeping coach) and Brad Friedel's disposal.
"That pitch, that atmosphere, that gives you desire to play. Moreover we got three points that made us start our season.
"For me, it is a period to manage. Obviously I have desire. I came here to play.
"I am at the club, I know where I have to go to. I had a talk with the coach, as he said, and I know everyone at Tottenham wanted me to come.
"So indeed, I am in an adaptation period, I've had very few training sessions, and there are players that I didn't know. But I am expecting time on the pitch."
Lloris had previously been warned by France boss Didier Deschamps that he could lose his place should he fail to secure first-team football, but the 43-year-old later retracted the claim.
It is possible that the former Lyon keeper could make his debut against Lazio in the Europa League on Thursday, with the north London outfit's fixture schedule building up, something that the Frenchman reiterated he is ready to do.
"I came to play," the 25-year-old added.
"This period is a bit strange. I'm ready, I want to play."