The West Indies won the Group D clash at Sabina Park by 54 runs leaving Pakistan, the 1992 champions, needing to ensure their place in the second round Super Eights by beating Zimbabwe and Ireland.
Victory on Tuesday also gave the hosts a crucial two points to take through to the Super Eights stage
"It was our goal to take the two points through but we now will have to do the hard yards," said Woolmer.
"The first goal is to get into the Super Eights and then let's see what happens from there."
Pakistan's build-up to the World Cup has been dogged by problems.
Pace spearheads Shoaib Akhtar and Mohammad Asif, who were both at the centre of a doping scandal, were ruled out on the eve of the tournament because of injury. Experienced all-rounder Abdul Razzaq also limped out of contention.
But Pakistan would have fancied their chances of victory on Tuesday after restricting the West Indies to a modest 241 in their 50 overs.
Woolmer admitted his team's batting just wasn't up to scratch.
"Our batting was disappointing because the West Indies bowled with great discipline and we struggled to get on top," said the coach.
"But like all games there were a number of crucial moments. Ramnaresh Sarwan (49) and Marlon Samuels (63) were two important innings although I thought generally we bowled and fielded well.
"It's too early to talk about being in tight corners. Let's make sure we remain positive for the rest of the tournament."
Pakistan face debutants Ireland on Saturday and Woolmer said he was impressed by what he saw when they had South Africa struggling at 92-8 in a warm-up last week before the world number one team recovered to claim a narrow victory.
"I have watched Ireland and I have been impressed by their discipline in the games against South Africa and Canada. I will watch them on Thursday (when the Irish face Zimbabwe) again after our practice."
Earlier Wednesday, Pakistan skipper Inzamam-ul-Haq blamed his experienced batsmen for the demoralising defeat to the West Indies and demanded they come good in the remaining matches.
"Our middle order is a very experienced batting line-up and we should have taken more responsibility in the opening game of the tournament," said Inzamam.
"There is some pressure on us now, but we will regroup and come back for the next match."