Atletico are in 14th place after managing one point from their opening two LaLiga matches - a 2-1 loss at Espanyol and a disappointing 1-1 home draw against promoted Elche.
Simeone's side now face the tricky task of visiting ninth-placed Alaves on Saturday, with their Basque opponents buoyed by three points from last week's victory over Levante.
When asked at Friday's press conference about his team's struggles, Simeone remained philosophical.
"It's always difficult to give scores to the work being done with so many new people," he said, referring to the arrival of the likes of Thiago Almada, Johnny Cardoso, David Hancko and Alex Baena in the close season.
"The team has worked well in these matches, with areas for improvement, especially defensively," added the Argentine, who acknowledged the pressure but insisted on staying calm.
"Anything less than picking up points is not positive, especially in our position," Simeone said.
"We have to focus on improvements, on continuing to build on what went well and, above all, on staying calm. In difficult times, we have to face them calmly in order to play the game the way we want to."
Simeone added that Atletico remain active in the transfer market with just days remaining before the window shuts.
"As always at the end of the transfer window, we are keeping an eye on everything until the last day," he said.
"I'm completely open at this stage to someone coming in or leaving, always with tension and talking daily with the board to finalise the squad as we need to."
Looking ahead to Saturday's clash, Simeone praised Alaves.
"They have a strong pace and they are very strong on their home turf. They have played two good matches, their coach (fellow Argentine Eduardo Coudet) has very clear ideas, and we hope to take the match where we believe we can do damage."