Inzamam feels his batsmen will need to come good in the remaining matches if Pakistan are to repeat their 1992 World Cup triumph after his side failed to chase the hosts' modest total of 241 at Sabina Park here on Tuesday.
"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 captain Inzamam.
Before a capacity crowd at the renovated Sabina Park, West Indies had a memorable start to the first ever World Cup staged in the Caribbean, when they bowled Pakistan out for 187 in 47.2 overs to clinch victory
"We should have got those runs because I think 242 was a gettable score," added Inzamam.
"We thought we could have chased those runs and we should have successfully chased them."
Pakistan were 39 for three at one stage, but Inzamam scored 36 and Mohammad Yousuf made 37 to put them back on track before Dwayne Smith, who was named Man-of-the-Match, claimed them both to end with three wickets for 36 runs from his 10 overs.
"Mohammad Yousuf's wicket was crucial, but we lost three early wickets, and we could have done well if we had more wickets left at the end," said Inzamam.
"We just didn't chase properly enough and West Indies bowled a good line and length.
"There is some pressure on us now, but we will regroup and come back for the next match."
Pakistan must now beat Ireland on Saturday, and Zimbabwe next Wednesday to guarantee they progress from Group D into the Super Eight stage of the competition.
Despite the defeat, Inzamam is confident his side will bounce back.
"There is something brilliant and magical about playing West Indies in West Indies, but we lost the opening game, and this is not very good.," he admitted.