Coming on the back of a 1-0 win at Nice that was marred by crowd trouble, Les Verts battered Reims 4-0 at Stade Geoffroy-Guichard on Saturday to move up to fifth in Ligue 1.
"It has been a difficult week in which we have not spoken much about football, but I dare say that tonight the image we gave of Les Verts was a good one," Galtier told reporters.
"It was an extraordinary match against a side who are tricky opponents when they play away from home, where they have lost just once this season.
"The team spirit and determination, both essential values at this club, were there today. It was a hard-fought game, but fair. I am very satisfied with the spirit shown by the players. It is a good victory."
Saint-Etienne travel to Rennes in their next game on Wednesday.