Gunness said the agency was trying to get material into a school for blind children but that it had been barred.
"These blind children, as far as I am aware, are not firing rockets. And the material we are trying to get to them would make a pretty floppy rocket if they tried to make one from it," Gunness said.
"We have a situation where hundreds of thousands of ordinary people, including blind children who would have been assisted, are effectively being punished for the irresponsible acts of a few."
"They are telling children in Gaza that they have to respect rights universally. How can we tell those same children, 'Oh by the way you have to respect rights of people in Israel but they are actually stopping us giving you food?"
Christopher Guness, UN aid agency spokesman
He added: "We condemn the firing of rockets. We do it every single time ... We cannot punish whole communities. This has got to stop. The blockade against the UN itself has got to come to an end."
Gunness said a team in Gaza was starting a human rights education programme in the run up to the 60th anniversary of the Declaration of Human Rights, but he added that it would be hard telling children to respect people's rights.
"They are telling children in Gaza that they have to respect rights universally. How can we tell those same children, 'Oh, by the way, you have to respect rights of people in Israel but they are actually stopping us giving you food?' It doesn't make sense," he said.
Gunness said the agency had made phone calls and sent emails seeking permission to deliver aid to Gazans, but it was getting no response
"We are told it is not possible ... it is difficult ... this stuff and the other. This sort of prevarication is leading to misery. A population is being radicalised in the Middle East," he said.
On Tuesday, Israel partially renewed fuel deliveries to the Gaza Strip, ending a week-long suspension of supplies that led to blackouts in the homes of Palestinian families.
Palestinian workers said the first delivery was received at the Nahal Oz fuel depot and was sent on to Gaza's only power plant.
The plant shut down on Monday due to what Palestinian officials said was a lack of fuel, leaving about half of Gaza's 1.5 million residents without power.
An Egyptian-brokered ceasefire that began in June has been disrupted following the imposition of the blockade.
Israeli's foreign ministry accused Hamas, which controls the Gaza Strip, of exploiting the situation for political gain.
"The cynical Hamas exploitation of the civilian population in Gaza is contemptible," a ministry statement said.
Kanan Obeid, a Gazan energy official, criticised the move as an example of "Israel's policy of collective punishment".
The Gaza City plant provides about a quarter of Gaza's electricity, while most of the rest comes over lines from Israel. Egypt also provides a small amount.