Ranieri: Greece lacked concentration
Jamie Ward and Kyle Lafferty were both on target for the visitors as Greece crashed to their second defeat in Group F.
Greece - the 2004 champions - are already eight points adrift of unbeaten Northern Ireland after three matches.
Speaking to reporters post-game, Ranieri said Greece were left to count the costs of their lapses at the Stadio Georgios Karaiskakis.
"We lacked focus at the start and conceded early on which made it difficult for us," said Ranieri.
"It was very difficult to break down a side so compact in defence. They are a team that know only too well how to close down space.
"We got hit by counter-attacks and had no balance in midfield. It was concentration that we lacked tonight."
Ranieri added: "I watched Northern Ireland's matches against Romania and the Faroe Islands and told my players to beware of set-pieces and counter-attacks – and that's how Northern Ireland scored.
"We conceded in Finland from a counter-attack and it happened again tonight."