The Eagles more than held their own against a Spurs side widely tipped to challenge for a top four finish this season as they made their return to Premier League competition.
Ian Holloway was always going to make his side hard to beat, and Tottenham did struggle at times to break Palace down.
A second half penalty from Roberto Soldado ultimately handed them all three points on derby day at Selhurst Park, but Ward believes Palace offered enough to suggest they are capable of competing with English football's elite.
He told Sky Sports: "After the game, I think we have got all the ability to go on and pick up points and to give this season a really good go. I think we will have some upsets in those big games.
"As a group of lads we have got a fantastic bond and we are all very together. That's what is going to help us through the season."
Fortune did not favour Palace in the award of the spot-kick which ended up costing them dear, with Dean Moxey pulled up for hand-ball, and Ward feels the result could have been different if big decisions had gone the other way.
He added: "I think it was a great opening day. We played well as a team, we defended well as a team, and we were unlucky not to make more of our chances.
"The game plan was working. In the lead up to the penalty, I haven't seen it, but there's talk that we maybe could have had a free-kick. It's just unfortunate that Dean's arms went up when he went to tackle him (Aaron Lennon)."