Slutsky's side will also face England in Group B, taking on Roy Hodgson's side in their first group match in Marseille on June 11, and he admits that he is intrigued by the match-ups his side have been given.
He admits, however, that he will have to research both Slovakia and Wales ahead of this summer's tournament.
"We've got a very interesting group," Slutsky told Uefa's official website.
"Of course, England are favourites in the group, but I think every team has a chance of making it through to the next round.
"So I think the matches in our group will be very interesting. There are no weak teams at the European Championships.
"In terms of our preparations, some of the teams’ playing styles are more similar than others.
"We don't know a huge amount about Slovakia or Wales because we've not come across them in official matches or friendlies.
"Now we will start actively gathering information."
Vitaly Mutko of the Russian Football Union added: "We will aim to progress from the group – we will see what happens.
"As for the group, it is a good draw and we are able to get through it. It is an even and competitive group."