The former Barcelona star has hit the ground running with his new club and his manager was left impressed with what he saw
Suarez was brought on in the 70th minute and marked his Atleti debut in style by netting an impressive double and setting up fellow substitute Marcos Llorente on Sunday.
The Uruguay international, who only joined in a €6 million deal from Barcelona on Friday, also won a penalty that was overturned by VAR in a one-sided La Liga contest.
Suarez scored with two types of finishes – one a brilliant header and the other a cute first-time finish on the rebound – but head coach Simeone was most pleased by the way his new forward teed up Llorente with only his second touch of the ball.
“His two goals didn’t stand out for me, but his assists, his runs and his movement did,” Simeone said after the match.
“The changes gave us a bit extra with the strength of Marcos, the quality of Vitolo, the clarity of Thomas [Partey] and Suarez knows what he has to do: play for the team.”
Diego Costa, Angel Correa and Joao Felix were also on target for Atletico at the Wanda Metropolitano as they recorded their biggest win in an opening league game under Simeone.
Atleti have been tipped to rival Real Madrid and Barca for the title this term and Simeone is hopeful that increased competition for a starting spot can get the most out of his players.
“It will depend on our work, our squad depth and the players’ security. The team was liberated,” he said.
“The arrival of an important player improves the team, but the team was already working very well. Now we’ll continue taking it game by game, like always.
“Suarez’s arrival generates a very good internal competition and if the 23 players accept the minutes they’re going to get, I’m sure we’ll compete well
“From my perspective, when it comes to building a squad, I look for guys who know how to perform and who accept when they play and when they don’t.
“That’s how great teams are formed. That’s what gives you the possibility of having more options. That’s what we’re looking for season by season.”