The Hoops are in Kazakhstan for the first leg of their third qualifier today and play a club who are top of their domestic league and well into their season.
However, Stoilov, who confirmed captain Tanat Nusserbayev would be out for a month with a knee injury, claimed his side were underdogs against Brendan Rodgers’ side.
The former Bulgaria player and manager said: “I know that Celtic play very well and are a very strong team. Celtic are favourites but we will try as much as we can and we will see what the result is tomorrow. They are favourites because they have big history at the club. They have been champions of Scotland many times and they have very many traditions.
“I have enough information about Celtic. I know the players, I know the coach, I know the history of this club. I know enough about the Scottish champions.
“It is going to be a very hard game for us. We are going to play a defensive game. We are preparing very well, but we have problems. We will try to do our best.”
Celtic lost 2-0 at the Astana Arena three years ago when they played Shakhter Karagandy in the first leg of their Champions League play-off but recovered in the second leg with a 3-0 win.
Stoilov, though, is not placing too much importance on the first leg at the 30,000-capacity Astana Arena, which has an artificial surface.
He said: “Yes, Shakhter from Karagandy played against them three years ago and three or four of our players were involved against Celtic at that time.
“It’s not important who will win tomorrow, it is important who will pass into the next stage.”