The principality club slipped to their seventh defeat in just 12 league games as Mathieu Cafaro's first-half strike proved decisive for Reims.
Henry replaced Leonardo Jardim in the Monaco hotseat in October and the Arsenal and France legend is still waiting for his first win in charge of the struggling side.
Monaco have picked up two draws and two defeats in Henry's first four games in charge in all competitions.
And the Frenchman warned his players that the situation will become more "complicated" if they fail to improve their form soon.
"This defeat is more worrying than the previous ones because we did not know how to create in the game and we did not get an opportunity," said Henry after the game.
"Reims practically won all of their duels and played as they should at home. On our side, the desire was not there.
"We have the chance to end up at 11 against 10 while we are not in the game and we punish ourselves with this second yellow [for Pele, in the 71st minute].
"It is a difficult situation and there are still many things to be done. After, if a gap is growing with the teams above us, it will start to be more complicated.
"The most important thing is to regain that confidence because the guys are not free.
"With the injuries we have, we must find a way and the best tactical scheme. Me too, I'm learning, it's only been two weeks since I've been there."
Monaco have been down to 10 men in both of their defeats under Henry, with Samuel Grandsir and Pele receiving their marching orders against Strasbourg and Reims respectively.