Martin O'Neill's side were denied a victory over Netherlands on Friday after Luuk de Jong's late equaliser cancelled out Shane Long's goal in Dublin.
Despite the disappointment of conceding late on, the draw extended a promising run of form for Ireland, in which they have suffered just one defeat in their last 13 matches in all competitions and kept six clean sheets.
Those results have increased belief within the Ireland camp that they can make far more of an impact in France than they did in the finals of four years ago, when they lost all three group games to Spain, Italy and Croatia and finished with a goal difference of minus eight.
And Coleman, who missed out on the squad in Poland and Ukraine, says the team spirit showed by Leicester during their fairytale Premier League title triumph must be a reference for his own side going forward.
"We're a hard team to beat and we can score goals," he said, as quoted by The Guardian. "Everyone wants to work hard for each other and a lot of that comes from the manager. He gives us time away from the hotel now and again and we appreciate that. It's like you want to reward him for how well he is with us.
"I'm sure everyone references Leicester City, and what a fairytale that was. Every one of them got back into position and it was a lesson for all the talented teams. There might be more talented players at club level but I'd rather have lads that work hard."
O'Neill is expected to rotate his side to give some fringe players the chance to impress, with the deadline to announce his final squad to take to France at 2300 local time on Tuesday.
James McCarthy (thigh) is not likely to be risked, meaning Darron Gibson, Harry Arter and Eunan O'Kane will all hope for another chance to impress from in central midfield – a position which O'Neill has already identified as a potential problem area.
For Belarus – who are set to be without Yegor Filipenko, having picked up a knock – the importance of the match is to recapture the discipline that saw them go five games without defeat prior to last week's 3-0 loss to Northern Ireland.
"It's hard to talk about the match," said head coach Aleksandr Khatskevich. "We played some intelligent football but we conceded goals from technical errors from individual players.
"Northern Ireland play simple football but we weren't prepared. But we have a direction to move in and we can't depart from that because of the defeat."