A late penalty was Suarez's second strike of the game and secured a 2-1 win over Eibar on Thursday night, taking the striker's haul to 11 goals in 14 league games.
Such has been the Uruguayan's impact since arriving from Barcelona, it even sparked a post-match question to Simeone as to whether he might be the coach's best signing.
In a little over nine years in charge of Atletico, Simeone has brought a host of notable players to the club, with Jan Oblak and Antoine Griezmann among them.
Simeone recognises Suarez's impact, but he was reluctant to compare the signings he has made during his reign.
"I don't stop in mid-season to think about such an argument," Simeone said. "He is amazing and we are very happy that he is with us.
"He is a great player with great characteristics. He knew how to play the game and gave us an important victory with a great defensive effort from the team."
The handsome lead that Atletico now hold over second-placed Real Madrid makes them favourites to land a first LaLiga title since 2013-14. They even have a game in hand.
But rather than take glee from toiling rivals Real Madrid exiting the Copa del Rey to third-tier minnows Alcoyano on Wednesday night, Simeone said such a result served as a reminder there are no certainties in football.
"It makes us pay attention and understand that football is more complex every day," Simeone said.
"Barca also won [against Cornella] in extra time ... Bayern [Munich] also lost in their cup, football is not simple.
"The opposition compete, they do it well and it makes us always be alert. Football is wonderful because it always gives you the chance to win."
Suarez, who sits third on Barcelona's list of all-time leading scorers, was a remarkable close-season acquisition by Atletico.
He has now scored 12 times in LaLiga against Eibar, more than he has managed against any other team.
The one-time Ajax and Liverpool frontman has looked sharp for his new team and puts his success down to the warm reception he was given, having at one stage appeared reluctant to leave Barcelona.
"I'm very happy. The team has been very welcoming," Suarez said. "They make me feel at home. I try to help the team the best I can, but we are all doing it too.
"We are showing everyone that we want to fight for important things.
"We need to keep working. We need to keep fighting for all the goals we set at the beginning of the season."
After Falcao and Griezmann, Suarez becomes new Atletico goal hero
It will be how well he sustains his early form that dictates how Suarez is eventually remembered at Atletico, but there can be no denying he has made a spectacular start.
He is averaging one goal every 92.18 minutes in LaLiga and has a 25.58 per cent shot conversion rate in the competition.
No player with more than one league goal during the Simeone era has a better average minute-per-goal record than Suarez, although Radamel Falcao comes close, with his 43 LaLiga goals under the Argentinian coach coming at one every 109.58 minutes.
Of all the players with more Atletico goals than Suarez in Simeone's time as coach, only Kevin Gameiro (27.14 per cent) has a better shot conversion percentage.
Suarez has so far had 13 goalscoring opportunities defined by Opta as 'big chances' and has gobbled up eight of those for an immensely healthy 61.54 per cent strike rate, better than any Atletico player with 10 goals or more in Simeone's time.
Griezmann remains Atletico's LaLiga leading scorer during Simeone's tenure, with 94 goals from 180 games, snaffling 53.04 per cent of his 115 big chances with an overall shot conversion rate of 21.22 per cent.
Only across one season of his Barcelona career did Suarez score at a faster rate in LaLiga than he has to date for Atletico.
In the 2015-16 campaign he plundered 40 goals from 35 games at a clip of one every 78.75 minutes on the pitch.
He eclipsed Lionel Messi in the scoring stakes that season as Barcelona edged out Madrid and Atletico in a three-team title battle.
This term, Suarez, who turns 34 on Sunday, is threatening to barge the Clasico giants out of contention and help Atletico make it a one-horse race.