Steve Smith's side completed a sweep of the two-match series with a seven-wicket victory at Hagley Oval on Wednesday which ensured they claimed the top ranking in test cricket.
"We certainly felt that we had a chance, without doubt," Hesson told reporters in Christchurch. "To lose the series two- nil was very disappointing.
"We weren't close in the end result but certainly felt that if things had been a little different then we might have been able to put a bit more pressure on them."
Australia's bowlers had created pressure on New Zealand's batsmen, initially courtesy of winning the toss and getting first chance on the green pitches, which assisted them.
Later in the innings, however, they also found significant and consistent reverse swing, something Hesson said his side had been unable to do.
"I think Australia were better with the ball and were able to generate movement throughout the match not just the first innings," Hesson said.
"At times we got it to go (reverse swing), but we didn't get it to go as consistently as Australia did and they got it to go a lot earlier than us."
He added that the pitch and conditions had not helped his side, with the Australians batting at optimal times to build big totals.
Australia passed 500 twice in their three innings with four of their top five scoring a century, while New Zealand's highest score was the 370 they posted in Christchurch when McCullum belted the world's fastest test century from 54 balls.
"The top five of Australia outplayed us," Hesson said.
"We were unable to break them down and get wickets in clumps which obviously Australia were able to do. To be fair I think their top five batsmen were exceptional."
