The Argentinian enjoyed a superb season last year when a return of seven goals and 16 assists from midfield was last week rewarded with an enhanced contract until 2018.
Di Maria is confident the Bernabeu side will improve and are set to add to the silverware - with the Champions League title also very much in their sights.
Di Maria told Marca: "I think the team is very strong. We have finished the pre-season in great shape and full of enthusiasm.
"The manager has told us the work we've done this summer has been incredible and the team really believes in itself.
"We have the capability to go places, to win more titles. We get better with each season and I hope this year we'll go a step further.
"On the back of the way we've worked and with the players we have in the team, I think there aren't any limits."
Valencia's Portuguese defender Ricardo Costa has called on his team to try and get a positive result at the Bernabeu in order to start well in a campaign where Los Che will hope to close the gap to Madrid and Barcelona.
Costa said: "It's the first league game and they are at home, but we must play our game, get our new signings to gel with the team and start the season with a good result to try to bridge the gap in the table with Real Madrid and Barcelona.
"We know they have their philosophy and spent three years with Jose Mourinho.
"They will start off strong, try to pressure us and create a goal in the first 15 minutes, but we must also start well, be strong and take the risks we have to take."