Defeat at Dublin's Tallaght Stadium on Wednesday (kick-off 3pm) would leave King's side with a mountain to climb to reach the finals in the Czech Republic next summer.
King said: "We want to keep the journey going to the end of the campaign.
"We always want to win every time we play, but we need to ensure we pick up the three points to keep things going in the competition.
"Everybody knows Montenegro are a good footballing nation who have caused trouble to everybody they have played. However we drew 0-0 out there and we created enough chances to perhaps have won the game.
"I'm expecting a tough game, but we are looking for a good all-round performance and a good spirit. If we get that, we will have enough about us to win this game."
The Republic currently lie in third place in Group 6, level on eight points with the Montenegrins, but behind on goal difference with leaders Germany six points clear.
However, Wednesday's opponents have played one game fewer, and the result of the encounter in Dublin could have a major bearing on how the race for second pans out.
The 10 group winners and four best runners-up will progress to the play-offs, from which the seven winners will join the hosts in the finals.