The victory takes the Blaugrana to within two points of leaders Atletico Madrid in the table, knowing that they play Diego Simeone's side on Matchday 35.
"It's a big step towards the title," Koeman said at the Estadio de la Ceramica.
"Each win is a step in the right direction. Each game is difficult.
"We reacted well to going behind and created chances.
"We were tiring in the final stages, but we defended well.
"We know that, with six games to go, if we win all six, we're going to be champions.
"But I think our opponents are going to make life difficult. We've still got to play Atletico.
"There's a long way to go, but we're going to give everything to try to win."
"I've always been delighted with him, with his work," Koeman said on Griezmann.
"He's improving his finishing and he was key today to being able to come from behind.
"This will give him and us confidence. We need players like him."