翻译：他的话使我认识到我错了.
what he said是主语从句,做convinced的主语,他陈述的是一个（过去、现在或者将来）的事实.
主语从句的时态,不受主句的时态影响和限制,所以不能因为convinced是过去时而said必须用过去完成时.
类似例句：That he finished writing the composition in such a short time surprised us all.
另外,这句话有错误：应该是
what he said convinced me that i was mistaken.convince sb + that clause使某人相信……
或者
what he said convinced me of my mistake.convince sb of sth使某人确信某事