Los Rojiblancos missed a chance to go top of the table as they were held in the matchday 10 fixture away at Estadio de Mendizorroza.
After taking a 70th-minute lead through Alvaro Morata, Atletico appeared on course for a win until seven minutes to full-time when Lucas Perez drew the hosts level.
“It was a tough match," Partey said of the game as reported by his club's official website.
"They’re strong at home.
"We took the lead, but they equalised through a fantastic goal.
"We have to keep working hard."
Partey was a 46th-minute substitute in the game, replacing Marcos Llorente.