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Megson's men, who struck the Chelsea woodwork twice and forced Carlo Cudicini to make a truly breathtaking point-blank save, now look like being involved in the relegation fight.
But Ranieri insists both teams proved their worth.
"It was difficult for us to pass, because they had a lot of players on the edge of their box," he said.
"It was very important for us to break their lines, and the match was better for us after we scored a goal. I'm happy and pleased with my players."
The visitors' spirited showing was no surprise to Ranieri, who added: "I watched two West Brom videos and already had a very good impression of them.
"I knew they would be a real threat. All their players play together and they work very hard.
"They played as a very, very united team and were good on the counter-attack - which was very dangerous for us.
"If they continue to play as well as they are now, I think they can stay in the Premiership."