Frankly, I have found very little evidence that anyone at all was surprised by this, or by the claim. Generally speaking, though Israel claimed to have been attacked, the overarching focus remained on why the war broke out and whether it was a justified preemptive attack, and Israel gave up the charade fairly quickly. It appears it was meant merely to distract international observers who might try to intervene early-on, so Israel could break the Egyptian forces apart and end the blockade that Egypt had placed on Israel in the Straits of Tiran while pushing back Egyptian forces massed on Israel's border.

The US received this claim from Israel in a notification at the start of the war, but US intelligence services managed to reveal that Israel has in fact launched its preemptive strike. They passed this information to President Johnson well before President Johnson had even notified Congressional leaders about the outbreak of war. He was thus not only able to tell them how the war began, he also could tell them (honestly) that he had expected it too, since the Israelis had been warning that the blockade and masses of troops on Israel's border would lead to an Israeli preemptive strike for weeks prior to the outbreak of fighting.

News reports were likewise nonplussed by day two of the fighting. An article in the Chicago Tribune spoke about Israel's attack, and outlined the fighting overall, on June 6. Most papers on June 5 did not report one side or the other as correct, and reported instead that both sides claimed the other attacked first. The UN's people on the ground also received Israel's claim, but contrasted it with reports that Israeli forces were attacking Egyptian positions in Gaza, and quickly discounted it.

So as far as I can tell, no one was really fooled, and the goal of giving Israel a few hours of diplomatic cover was largely successful. This type of thing is not uncommon in war, for the record, including between Arab states and Israel, so it seems like most countries simply moved on from it quickly.