After problems for Ferrari team-mate Raikkonen and Sebastian Vettel, Alonso chased Daniel Ricciardo for third, but suffered brake issues in the closing stages.
"At the end we had some brake problems," said Alonso.
"The car was braking with only right brakes so I had to hold the steering to the left.
"Once you are in that position you just try to bring the car safely home and get these points, but obviously we will try to do better next time."
Despite the issues, Alonso believes fourth was the best the F14 T could manage in Monaco.
"Fourth was the maximum," he said. "The top three showed their potential and that they were faster than me.
"I'm happy with the weekend in general. The race was difficult, it was tough, but I've got more points than I had yesterday."