In a special Commons statement, Mr Straw announced he was taking the extraordinary step of personally deciding on any applications, in a bid to head off right-wing criticism that Britain was seen as a "soft touch" on asylum seekers.
"Subject to compliance with all legal requirements, I would wish to see removed from this country all those on the plane as soon as reasonably practicable," he told the Commons.
"As a matter of public policy, I believe that the clearest and unequivocal signals must be sent out so as to discourage hijacking, whatever its motive," Mr Straw said.
"While I must and will act in accordance with the law, I am determined that nobody should consider that there can be any benefit to be obtained by hijacking."
Of those on the plane, 60 had so far told immigration officers they wished to apply for asylum along with 14 dependants. The remainder had yet to make their wishes known.
Mr Straw pledged to "respond resolutely to any attempts like this to use terrorist methods, whether the aim is to advance a political cause or to benefit the individuals concerned".
He explained that the hijacked plane had been allowed to land at Stansted in accordance with Britain's "international obligations". There had been "serious concerns about the safety of those on board, given the threats that had been made earlier to kill passengers, uncertainty over fuel levels and reports of technical problems".
Mr Straw said no political demands were made at any time following the plane's arrival at Stansted, although statements were made to negotiators about the political situation in Afghanistan.
No undertakings "of any kind concerning asylum" had been given by government representatives during the negotiations and "the surrender from the plane was unconditional".
Shadow home secretary Ann Widdecombe told MPs a deterrent to future hijacks would be to ensure Britain's asylum procedures were not "noticeably softer" than those in surrounding countries.
"Why the United Kingdom?" Miss Widdecombe asked. "Why did it decide that it would land here and try to take advantage of our asylum procedures? Is it that those procedures are known to be rather more congenial than some which appertain in other countries which are nevertheless still signatories to the 1951 convention [on refugees] and to the ECHR (European court of human rights)?"
She welcomed the home secretary's decision to decide the asylum applications personally but stressed that speed was of the essence.
Mr Straw agreed speed was important in processing asylum seekers' claims and said special arrangements had been put in place with that aim.
Liberal Democrat spokesman Simon Hughes said rules should be set down if the home secretary was going to start "calling in" immigration and asylum applications on a regular basis, as he recently did with boxer Mike Tyson.
"Can we have rules that govern that just as one does for calling in planning applications, rather than you simply being able to pick and mix with nobody knowing whether they are going to get special fast treatment from you or the normal treatment from somebody else?"
