Speaking shortly after the All Blacks retained both the Bledisloe Cup and Tri-Nations trophy in torrential conditions at Eden Park, Connolly insisted there was still little to choose between the two sides.
"I probably think at times there is not much between the two teams. Most games swing on close decisions. We saw that in Melbourne and we saw that here," he said.
"I don't think [the All Blacks have the edge] at all. I think it is one game each this year and I think players from both sides realise that it was a close game.
"I don't think it has a great bearing at all."
A crucial moment in the match came when Wallabies skipper Stirling Mortlock was penalised for a high tackle midway through the second half - a decision which eventually opened the door for the All Blacks to score the match's solitary try.
And after time to reflect on the indiscretion, Mortlock admitted the mistake had proved costly in the overall scheme of things.
"I think in big games, little things can have massive repercussions and I was a little bit disappointed that that one did seem to turn the game," he admitted.
"The decision was made at the time and they seemed to get a leg up from that.
"I think currently you have got to play what is in front of you and play how the referee interprets the rules on the night and I think the All Blacks did that a lot better than us tonight.
"When you play a team as good as the All Blacks you can't afford to let them get a leg up."
Victorious coach Graham Henry, having retained the two trophies for another year, admitted the side was aware of how much it meant to the country to put on a good performance.
"Obviously we are pretty happy to win the Bledisloe Cup and Tri-Nations trophy again," he said.
"It's very important to the team and very important to the country and I think the Bledisloe Cup is probably the trophy that people value the most."