The Black Caps were about to clock up a victory over the West Indies at University Oval on Saturday before rain arrived and robbed them of the chance.
McCullum is yet to bag a win as captain in 10 tests, and it was once again so close yet so far on Saturday.
''You are judged by your results and we have not won a test since I have taken over. And obviously that frustrates you. We did everything we could to win this test match,'' he said.
''I believe we would have won this test if it did not rain. It was similar to the test match last year, against England, where we did all we could to win the game but it did not go our way. We have had some lows during this time but I firmly believe we are performing pretty well in test cricket and sooner or later the wins will come.
''We just have to persevere in what we are doing and get the odd slice of luck to go your way and those results will follow. You certainly can't try and reinvent those results because you are so close to getting them.''
He said it was obviously disappointing to not win on Saturday, after playing some good cricket throughout the week in Dunedin.
''To get 600 and then set the game like we did, we gave ourselves an opportunity. It was just disappointing when it started raining when we were only 33 short.
''We never got ourselves in the position in the chase to put the hammer down. A couple of us played some pretty poor shots, trying to find the balance between being positive and still trying to get ourselves through.''
He did not calculate for the rain coming, and felt weather watching was not a great strategy when chasing.
McCullum, though he went cheaply in the second innings, was relieved to have bagged a century in the first innings, after a lean run.
''I don't think I have played under so much media and public scrutiny in my career. To come out the other side of that and score a hundred, with pretty tough external and internal pressure as well, was relieving, more so than pleasing.''
His well-documented back issues remained, and he would continue to manage the injury. He also hurt his knee when he crashed into an advertising board on Friday.
New Zealand faced a target of 112 to win in its second innings and was 79 for four wickets, needing 33 to win, before being forced off the field, five minutes before the tea break.
Over the tea break the rain got heavier, and once lightning and thunder was seen and heard after 4pm, the writing was on the wall.
The covers were lifted at 5.20pm but went back on again about 15 minutes later, as it started raining again. Another attempt was made at 6.05pm but the umpires ruled a draw as the covers were lifted.
It was a tough way to finish for the Black Caps, who had the best of the test, but could not ram home the advantage.
Saturday had started well, as Trent Boult bowled double century-maker Darren Bravo just over 10 minutes into the day. The ball failed to bounce, rolling along the ground.
Shane Shillingford then hung around, while his captain Darren Sammy continued to spray the ball around the ground.
Eventually, Sammy was down to the final man and when he tried to smash Tim Southee out of the park he succeeded only in skying a catch to deep point, dismissed for 80.
New Zealand came out 10 minutes before lunch and Fulton was out in the fourth over, caught behind off Shillingford.
The spinner added three other scalps in the second session but New Zealand was in the box seat when the heavens opened.
McCullum said he would look how his bowlers come through the next couple of days after bowling more than 220 overs in the match.
Kane Williamson, testing his injured thumb, scored a century for Bay of Plenty in Tauranga on Saturday and is likely to come back into the team for the second test. Otago's Aaron Redmond will presumably be released.
