The sending-off of captain Antonio Valencia for a dangerous challenge on Lucas Digne left the South American nation to play most of the second half with 10 men, while an apparent elbow by Mamadou Sakho on Oswaldo Minda in the first half was missed by Ivorian referee Noumandiez Doue.
"What happened was a shame. It is up to the committee that looks after these things to judge the performance of the referee," said Rueda of the latter incident. "A lot of his 50-50 decisions were not ideal."
"We lost an important player in our structure and it was difficult to hold on for a draw but thanks to the character of the players we did so."
The result combined with Switzerland's 3-0 success against Honduras left Ecuador as the first South American nation to be knocked out of this World Cup.
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Ecuador had beaten Honduras 2-1 in their second game last Friday, but Rueda admitted that their prospects of qualifying for the last 16 were compromised when they lost by the same scoreline to Switzerland in their opening match in Brasilia.
Enner Valencia put Ecuador ahead in that game only for Admir Mehmedi to equalise before Haris Seferovic struck an injury-time winner that ultimately proved crucial.