Wenger pinpoints Arsenal's run of two points from three games in late April as the end of their title challenge.
"I was happy with the attitude of the players and our away form," he said.
"But what was disappointing was that when we needed to push on, we could not show the nerves to deal well with some games.
"I'm thinking about Liverpool, Tottenham and Bolton. We had good opportunities to win those games and had we done, that would have been seven points more."
Arsenal conceded 41 goals in the Premier League with the set piece their Achilles heel, prompting Wenger to target some taller players in the transfer market this summer.
"We conceded very few goals from open play, most of them were from set pieces in a way you don't want to concede goals," he said.
"It's something that's easy to correct. We need to improve the size of our squad. We need a bigger variety in the height of our players.
"We need to be more capable of fighting against some characteristics than we have been this season."