Both teams fielded strong sides in the final game of the International Champions Cup at Atletico's home ground, with the likes of Antoine Griezmann, Thomas Lemar and Mauro Icardi all on display in the match.
Inter had several chances in the first half to take the lead, with Atletico keeper Jan Oblak needing to be on top form to stop Icardi and Marcelo Brozovic from scoring early on in the match.
However, in the 32nd minute of the match Oblak was beaten, when young Argentine striker Lautaro Martinez volleyed home emphatically to give his side the lead.
The home side had a goal disallowed when Angel Correa thought he had scored, but other than that they failed to break through the Luciano Spalletti's side defence.
Even with the introduction of Griezmann and fellow World Cup winner Lucas Hernandez in the second half, Diego Simeone's men could not find an opening and were denied by an excellent save from Samir Handanovic in the Inter goal just minutes from time.
Atletico will now concentrate on their European Super Cup tie, which takes place against rivals Real Madrid on Wednesday.