Having secured big-money moves for Toni Kroos and James Rodriguez, European champions Real sanctioned the respective departures of Di Maria and Alonso to Manchester United and Bayern Munich during the transfer window.
The sale of two of Real's stars of the 2013-14 campaign, in which Real won the UEFA Champions League and Copa del Rey, was met with some criticism by supporters.
However, midfielder Suarez - whose Atleti side meet Real in the Madrid derby when La Liga resumes after the international break - stated that Carlo Ancelotti's men remain a huge threat.
"[Real] Madrid are still playing well. They have lost important players but great players have signed," he told AS.
"They can mix direct football with possession football. Against a team like this you can't make any mistakes.
"For me Xabi Alonso has always been a benchmark , one of the best midfielders in the world. They have bought Toni Kroos, who is a great player. They're both very good.
"Angel di Maria is gone, but James Rodriguez is there. That's Madrid's advantage, they've been weakened but they keep fighting for everything."
Atleti surprised many last season by breaking the domestic dominance of Real and Barcelona by lifting the Liga title for the first time since 1996.
Suarez insists that the team have no intention of letting up following their success, adding: "It was very nice to make history but that is already behind us.
"We are judged by what we do from now on. We started well, with a trophy [the Supercopa de Espana] and in the league we have four points from a possible six.
"Historically this has been a big club. There was a time when things didn't go right but since the coach [Diego Simeone] joined we have been accustomed to playing big games and competing with the best.
"We believed we could win that title and most people didn't. But it went well."
