The Republic staggered to a 0-0 friendly draw with Northern Ireland at the Aviva Stadium on Thursday evening to extend their recent run to just one win in 10 games, but they needed keeper Darren Randolph to pull off two fine saves to keep the visitors at bay.
Ireland head into their final Nations League B, Group 4 game with Denmark in Aarhus on Monday having been booed from the pitch by their own fans, and captain Coleman knows there is only one solution.
"Look, as far as I'm concerned, we've got the best fans in the world. When we're doing well, they're unbelievable. But as players in that dressing room, we have got to weather the storm together now," he said.
"We're going to get criticised - take it on the chin, we have to take it on the chin. We weren't good enough tonight, so we have to take it on the chin.
"But we also have to man up and take responsibility as players, as professional footballers who are playing for our country. We have to take responsibility, myself included."
Ireland could already be condemned to relegation from their group by the time they kick off in Denmark, but Coleman is expecting a response whether or not the game is a dead rubber.
"Talking before games, talking after games, it's a load of nonsense, really. It's on the pitch that it has to happen, and that starts against Denmark. We have to end this year on a high," he went on.