Wales were impressive in qualifying for the upcoming tournament in France, with a haul of 21 points from 10 matches enough to see them through their pool in second place behind Belgium.
Coleman feels four points from three Group B games against Slovakia, England and Russia will suffice for Wales to reach the knockout rounds, and he is determined to get three of those on the board from their opening fixture with Jan Kozak's team.
"We're probably going to need four points to get through. Is that possible? Absolutely. Is it difficult? Yes," the Wales manager told Omnisport.
"The first game is Slovakia and that's all we're concentrating on. There's huge pressure on us in that first game. We want to get off to a good start - it's unknown territory for us, we've never been to a tournament.
"But the rules are the same, nothing changes there. We've just got to make sure we don't get carried away and do what we've been doing."
Neighbours Wales and England were paired in Group B and will face-off in a hotly anticipated clash in Lens on June 16.
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However, while insisting he does not fear their footballing ability, Coleman wishes Wales had avoided England at Euro 2016 due to the "circus" surrounding Roy Hodgson's side.
When asked about the importance of the England clash, Coleman replied: "It's pointless beating England if we don't get through - it doesn't mean anything. We've got to get four points, it doesn't matter how we get them.
"I know the attraction of England, but the thing that comes with England is the circus, which you don't want to be involved in - the hype and everything surrounding England.
"I obviously know Roy very well and he's someone I respect a lot. I didn't really want them in our group, not because we're afraid of matching up against them on the pitch, but I didn't want all the hoo-ha that comes with England off the pitch.
"But we're not thinking about England, we're thinking about Slovakia. Once we've dealt with them, then we'll deal with England."