The select committee chair had initially vowed to continue his "duties" as an MP after he was suspended from the parliamentary Conservative Party when he was revealed to be the man at the centre of the allegations.
However, he resigned on Saturday after he was supposedly told by allies his position had become untenable.
Asked by reporters if he opened something in error in the Commons, he said: "I did, but let the inquiry look at that."
There have also been suggestions that a Tory minister also witnessed him watching porn on a second occasion.
In an interview later conducted in his dressing gown on Friday night, Mr Parish told the Telegraph how "it's almost as if a weight is lifted off me" now the accusation is "out in the open".
Mr Parish referred himself to Parliamentary Commissioner for investigation and on Friday said he would only resign if found guilty.