The Toffees kicked off their 2018-19 season with a point against their newly-promoted hosts, despite playing more than half of the match with only 10 men following Phil Jagielka's contentious red card.
Richarlison marked his competitive debut for the club with two goals, and the Brazilian insisted that he will continue to give his all for manager Marco Silva.
"It was a very difficult match, we had to run double because we were a man down. One point away is very important," he told BT Sport.
"I know my responsibilities and what I have to do on the pitch for Marco Silva. I look to Marco like a father, he took me from Brazil to England. I'll be grateful for life to Marco."
Richarlison is the first Everton player to score twice on his Premier League debut since compatriot Jo in February 2009.