Fans' favourite Dominguez is headed to Borussia Monchengladbach for £8million.
Diaz told AS: "He (Dominguez) has played here, come through the academy and is important for the club but I have come here to do my bit and I have the same pressure all players have when they arrive at a new club. I don't think that my coming here and Dominguez leaving will bring me more pressure than the others.
"When a team like Atletico became interested in me I wasn't in any doubt. I am arriving with a lot of desire and happiness. I want to demonstrate that on the pitch because with words I can't say very much. I hope it will be a good year for the team."