But he also said that sharply higher oil prices have not produced any "serious erosion" of world economic activity.
"The United States, especially, has been able to absorb the huge implicit tax of rising oil prices so far," Greenspan told a Senate hearing in his first appearance before Congress since leaving the Federal Reserve.
"However, he added, "recent data indicate we may finally be experiencing some impact."
Greenspan said the high oil prices, exceeding $70 a barrel resulting in gasoline costs to sore beyond $3 a gallon, are due to a sharp decline in spare global oil production capacity, refinery shortages and to some extent market speculation.
He said that American business "to date has largely succeeded in finding productivity improvements that have contained energy costs." But he said consumers "are struggling with rising gasoline prices."
Greenspan, appearing before the Senate Foreign Relations Committee, said he saw little chance that the narrow gap between global oil supply and demand will expand anytime soon.
But he said "current oil prices over time should lower to some extent our worrisome dependence on petroleum" with the development of alternative fuels and broader use of electric-hybrid cars. This "would help to wean us of our petroleum dependence," Greenspan said.
He said the United States has been able to "absorb the huge impact of rising oil prices with little consequences to date because it has become far more flexible" over the past three decades because of less regulation and globalization.
But he warned against import or price restrictions or other interference in the market.
"Growing protectionism would undermine that flexibility and make our nation increasingly vulnerable to the vagaries of the oil market," he said.
Greenspan told the Senate panel that the issue isn't so much the supply of oil reserves. Rather, it is that few national oil companies are investing enough to convert reserves "into crude oil productive capacity."
"Besides feared shortfalls in crude oil capacity, the adequacy of world refining capacity has become worrisome as well," Greenspan said, noting that in the case of the U.S., there hasn't been a new refinery built since 1976.
One bright spot, Greenspan suggested, is that higher oil prices are acting to limit U.S. dependence on oil, a trend that has already been occurring since the 1970s. Between 1945 and 1973, U.S. petroleum consumption grew at a "startling" 4.5 percent per year, Greenspan said. That rate fell to just 0.5 percent per year between 1973 and 2006, he added.
"Oil in the years ahead will remain an important element of our energy future, but it need no longer be the dominant player," he added.
But outside the U.S., some trends point to continue robust oil consumption, especially in China, Greenspan said.
Motor vehicle use there "is gaining very rapidly," Greenspan said, while fuel efficiency in China is not a high priority given the country's desire to rapidly industrialize. Thus, China will remain a "major demander" of oil, Greenspan said.