Lloris' side secured a 1-0 win in Finland on Friday night before a man of the match performance in the 3-1 victory against Belarus on Tuesday.
But now the 25-year-old has his eyes set on securing a starting job for Spurs, despite manager Andre Villas-Boas revealing that veteran Brad Friedel is No.1 for now.
"Peacefully, I enjoyed both games with the national team and will now discover another world, another championship, another mentality," Lloris told reporters.
"It's all positive so I will have to get to know my team-mates, the staff and I will try to work as best as possible. There is a lot for me to prove in a new league, but I will work and earn success."