Barca secured victory via Frenkie De Jong's 27th-minute finish, with Lionel Messi providing a fine assist on his return to the team after an ankle injury – the Argentina superstar's 750th appearance for the club and 500th in LaLiga.
Koeman's men are now fifth in the table, 10 points behind leaders Atletico Madrid, who have played one game fewer.
Barca's next match is at Athletic Bilbao on Wednesday, and they are then at Granada three days later and Elche on January 24.
Koeman was quoted by Marca as saying in his post match press conference: "This month is very important for our aspirations because we have lots of games away from home and, if we win them, I think we can fight.
"We've seen this weekend that it's not easy to win away from home. If a team (above us) goes on a bad run, the gap can be closed, but it depends on us winning."
Barca only registered once despite numerous attempts on goal, including two Messi efforts that were well saved by Huesca goalkeeper Alvaro Fernandez, while the hosts went close through on-loan Wolves forward Rafa Mir and saw a late push for an equaliser prove in vain.
Koeman said: "We can improve on our final ball, on picking up positions inside the box.
"I'm happy with Frenkie's goal because we want our midfielders to get into the opposition box. We hope to be more clinical because you win games easier (like that)."
"I trust every player in our squad, but if we choose to have three central midfielders, there's room for three forwards," said Koeman, who brought Griezmann on with around 10 minutes to go.
"With Leo, we went for someone who gets in behind more like Dembele and we have to choose between Martin or Antoine up front.
"Martin did well. He's the number nine we need in these types of games but leaving Griezmann on the bench means nothing. We have lots of games and we need every player.
"(Dembele) is a player we need because we're missing Ansu Fati, who is also a striker who can play out wide. He gets in behind the opposition, he's good one-on-one...
"It's always important to have one who gets in behind to take advantage of the quality of Leo and the midfielders."