Athens was indeed a direct democracy. Any citizen of the city could vote and/or address the public assembly.
As far as losing to the Spartans, that WAS caused by direct democracy.
"In 415 B.C. Alcibiades convinced the Athenian assembly to vote to launch a massive naval campaign against the large island of Sicily1 to seek the great riches awaiting a conqueror there and prevent any Sicilian cities from aiding the Spartans. Formally speaking, Athens was responding to a request for support from the Sicilian city of Egesta (also known as Segesta2), with whom an alliance had been struck more than thirty years earlier. The Egestans encouraged Athens to prepare a naval expedition3 by misrepresenting the extent of the resources that they had to devote to the military campaign against non-allies in Sicily. The prosperous city of Syracuse4 near the southeastern corner of the island represented both the richest prize and the largest threat. In the debate preceding the vote on the expedition, Alcibiades and his supporters argued that the numerous war ships in the fleet of Syracuse represented an especially serious potential threat to the security of the Athenian alliance because they could sail from Sicily to join the Spartan alliance in attacks on Athens and its allies. Nicias led the opposition to the proposed expedition, but his arguments for caution failed to counteract the enthusiasm for action that Alcibiades generated with his speeches. His aggressive dreams of martial glory especially appealed to young men, who had not yet experienced the realities of war for themselves. The assembly resoundingly backed his vision by voting to send to Sicily the greatest force ever to sail from Greece. The arrogant flamboyance of Alcibiades' private life and his blatant political ambitions had made him many enemies in Athens,5 and they managed to get him recalled from the expedition's command by accusing him of having participated in a sacrilegious mockery of the Eleusinian Mysteries and being mixed up in the sacrilegious vandalizing of statues6 called Herms7 just before the sailing of the expedition. Alcibiades' reaction to the charges certainly was unforeseen: he deserted to Sparta."
The ability of a few men to sway the opinion of the uninformed public(the assembly was comprised of the Athenian citizenry) led them to send a monster of a military force across the Med to Sicily where it was utterly destroyed by Syracuse and a number of other small Greek cities.