Bangladesh failed to capitalise on a brilliant 84 by Shakib Al Hasan - the highest individual score by a Bangladeshi batsman in all Twenty20 cricket - which lifted them to a challenging 175-6 at Pallekele stadium on Tuesday.
Pakistan successfully chased the target on the back of a career best 72 by Imran Nazir and 45 by skipper Mohammad Hafeez to advance to the Super Eights round.
This becomes Bangladesh's second first-round exit from a major event in a year following their failure in the 50-over World Cup at home - which Rahim said were disappointing.
"It's always disappointing to go out of the tournament early," said Rahim after the match.
Bangladesh lost their first game by 59 runs against New Zealand, for whom Brendon McCullum hit the highest individual Twenty20 score of 123 in the first group D match.
"We have not played our best game in the first match so that put us under huge pressure in the second. Also, probably, we were nervous," Rahim added, before ruing the lack of quality in his team's bowling.
"We have spin bowling in our line-up but we did not get any spin in the wicket so that put us under pressure," said Rahim, whose team had three left-arm spinners in the match against New Zealand.
"Also in our pace attack we don't have quality bowlers like Pakistan's (Umar) Gul and (Sohail) Tanveer. If we had played better in first game that would have given us the belief," said Rahim.
However, Rahim said despite the losses he was happy at team's improvement.
"I am quite happy after how we raised our game in the second match and we must continue to learn for the sake of our future," said Rahim, who hailed his superstar Hasan.
"He showed that he is our best player. There is no doubt about it, it's a privilege to play with him. He is probably the best player Bangladesh has ever produced in my opinion."
Bangladesh host the West Indies for two Tests, three one-days and a Twenty20 match late next month.
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@Sumaiya: Sohail Tanweer is not a quality bowler?he was man of the series of IPL-1.....it was bowling pitch..
Sohail Tanveer - a quality pace bowler?? Hahahahaha! No offence...
hey,does n't matter,you played Well,that was a good fight,we love our Bangladishi brother but we were compel to win it cause we have to qualify for Super Eight...Well Played Shakib...Good Luck for your Future
BREAKING NEWS: tissue papers shortage is reported in Bangladesh after yesterday's match.