The Three Lions had to battle for a draw in Dunedin after being bowled out for 167 in their first innings, but took control in Wellington before the rain forced officials to rule the contest as a draw.
It means that the series is locked at 0-0 heading into the final Test.
"We got ourselves into a really good position to win the game," Reuters quotes Cook as saying. "We can take a lot from that [considering] our first performance.
"In Dunedin, we were behind the eight ball because we didn't bat well for two sessions and we did well to fight and hold on for that game.
"This game we played some really good cricket and gave ourselves a really great opportunity to win this game but the weather didn't allow us to do that."
The third Test gets underway in Auckland on March 22.