The Ryder Cup veteran, 41, finished two over par, two shots adrift of the projected cut and down in tied 93rd.
He needed to win at least £23,905 ($30,639) - equivalent to a top-30 finish - to retain his tour place.
But the 2008 Open runner-up said: "It doesn't mean you're never going to see me again."
He later added on Twitter: "You don't get to number five in the world and help lift a few Ryder Cups and disappear.
"You come back stronger and more determined than ever."
Scotland's Martin Laird, who won the Texas Open in 2013, remains in contention at the halfway stage in San Antonio.
The 34-year-old shot a second-round 67 to leave him five under par, three shots behind the joint leaders, American pair Bud Cauley and Tony Finau.
Northern Ireland's Graeme McDowell is two under but England's Luke Donald, runner-up in last week's RBC Heritage, missed the cut on four over.
First-round leader Branden Grace carded a one-over 73 to drop back into a seven-way tie for 10th, alongside Laird.
Poulter, who shot 75 and 71, said he would still play on the PGA Tour through sponsors' invites and add more European Tour events to his schedule.
The world number 190 added he thought his struggles had been "slightly over-dramatised".
"It means I've got some work to do and I need to go away and do some work," he said.
After missing the second half of last season with a foot injury, Poulter started this season needing to earn either 218 Tour points or £271,514 ($348,000) in 10 events to retain his full playing privileges.
He has accrued 155 points and prize money of £247,335 ($317,010).

Fish oil has been marketed to women as a prenatal supplement.
But a 10-year study of more than 2,500 pregnant women found it did not improve babies' intelligence, according to the Australian research.
The findings suggested that fish oil might lead to slightly longer pregnancies, but that would require further research, the team said.
"If a pregnant woman has a healthy, balanced diet, then the baby's brain development is not going to benefit from having these fish oil supplements," study co-author Dr Jacqueline Gould told the BBC.
The research, by the South Australian Health and Medical Research Institute, followed women from their pregnancy to when their children were seven years old.
Participants were given either a daily fish oil supplement or a placebo.
The results found taking a 800mg dose of docosahexaenoic acid (DHA), an omega-3 acid, had no impact on babies' intelligence.
Dr Gould said supplement makers had specifically marketed fish oil as a way to boost development in infants.
She said the research, detailed in the Journal of the American Medical Association, showed fish oil might be linked with longer pregnancies.
"What that meant was, there were slightly fewer children born pre-term," Dr Gould said.
"We're currently trying to validate that in a much bigger study."
England's Ian Poulter says he will "come back stronger than ever" after losing his PGA Tour card by missing the cut at the Texas Open.
[NEXT_CONCEPT]
Taking fish oil while pregnant does not improve the brain development of babies, new research has found.