Sage replaced Oliver Glasner during the summer and has had to manage a disrupted pre-season, with the World Cup and several late arrivals affecting his preparations.
Palace have taken four points from their opening five league matches, but Parish believes Sage has handled the circumstances well.
“After seven games, a record of three wins, three defeats and one draw is not a bad start at all. If you take into account everything he has had to deal with, he has done very well,” Parish told The Athletic.
The chairman also dismissed reports of tension surrounding Sage's handling of certain players.
“Everyone is on the same page and we are moving forward,” Parish said.
Parish has been particularly impressed by the football Palace are producing, pointing to improvements in their performances and the enjoyment of the players.
He highlighted the victory over Leeds as an example of the progress made under Sage, arguing that Palace produced a level of football that would have been difficult to imagine at the start of the campaign.
“Pierre, his staff and everyone have done a remarkable job to get us to where we are today,” Parish said.
The chairman also praised Sage's adaptation to life in England. The Frenchman is continuing to take English lessons, with Parish joking that “his English is better than he thinks.”