The 19-year-old defensive midfielder has joined the Premiership leaders on a four-year deal after a £2.8m fee was agreed with Russian club Krasnodar.
"All I'm interested in at the moment is really progressing," Kouassi said.
"I really feel this is the best place for me at the moment to progress, to become better."
Captain Scott Brown played his 400th game for Celtic in Wednesday's 1-0 league win over St Johnstone and Nir Bitton, Callum McGregor and Liam Henderson have also played in central midfield areas this season, with Stuart Armstrong and Tom Rogic tending to play further forward.
"I'm not getting worried about it," Ivorian Kouassi said through an interpreter.
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"At the moment, since I haven't played for a wee while, I need to get back to full fitness then after that the coach is going to decide.
"When you play alongside players with such experience, you learn a lot. I expect players such as Scott Brown to really help me and maybe guide me.
"There's lots of great players that have come to Celtic before. It's got a great, great coach at the moment."
Uncapped at senior level, Kouassi played in the Europa League with Krasnodar and has watched Celtic playing in the Champions League, including this season's matches in Group C, which also contained Barcelona, Borussia Monchengladbach and Manchester City.
"It's something that I'm really, really happy about because it's the top," Kouassi said on the prospect of playing in next season's tournament. "It's the best you can get in European football.
"This is going to have an impact. Celtic is not a small club so hopefully, this will have an impact on my international career with Ivory Coast."
New Celtic midfielder Eboue Kouassi is "not getting worried" about the competition he faces for a place in Brendan Rodgers' team.