Did John the Evangelist make a mistake in counting the post-resurrection apparitions of Jesus?

We see Jesus making his post-resurrection apparition before the disciples on various occasions: first, to the disciples on their way to Emmaus (Lk 24: 13-35), second, to the disciples in the absence of Thomas (Jn 20:19) then in the presence of Thomas (Jn 20:26) followed by the apparition at Tiberius (Jn 21:1). John specifies the Tiberius apparition as the third one (Jn 21:14), whereas it should have stood at 4th place, counting from the Emmaus apparition. My question therefore is: **Did John the Evangelist make a mistake in counting in order, the post-resurrection apparitions of Jesus? What does the Catholic Church say about such a prospect?**