McCullum's side had reached 162 for two in their second innings after being forced to follow on, though they were still 49 runs adrift from making England bat again.
Intermittent showers on the fourth day and persistent rain on Monday ensured the final match in Auckland later this week will be a series decider.
"It was a draw at the end of the day and, I guess similar to the first test match. If it's viewed as a points decision, I guess England will take this one," McCullum said.
"They dictated this one and we held on and showed some fighting qualities."
McCullum had actually won the toss on the first day and asked England to bat in the hope that the wicket would provide his seam attack with some assistance before it flattened out.
The visitors, however, batted New Zealand out of the match on day one with Nick Compton and Jonathan Trott scoring centuries, and McCullum said he felt that his side had not performed as well as they should have.
"I thought we were pretty average on day one. There was a little bit in the wicket that we could have got some more benefit from," he said.
"We probably didn't bowl as well as what we needed to for as long as what we needed to against some quality batsmen.
"Our execution was off. We didn't put enough pressure on England long enough and when up against a fine batting lineup got to be able to exert pressure for a long time.
"From that point on, we were under pressure (but) we managed to stand up and sustain some pressure that was exerted on us by England, which is a really good sign for this team."
England bowling coach David Saker had criticised the nature of the pitches produced in both Dunedin and at the Basin Reserve, which he felt allowed the batsmen to dictate the flow of the game, though McCullum said the weather had been more of a defining feature in terms of results.
More than 100 overs were lost due to rain in Dunedin, while more than 150 were lost in Wellington and McCullum said if play had been able to go for the full five days in each match criticism of the pitches would not have been made.
"It seems to be bowling coaches who have an issue with them. It's always going to be the way," he said with a grin.
"If we look at the first test match, we lost a whole day to rain. There would have been a certain result in that game - well, that's what I think - and then if you look at this test match as well, we lost a day and a half to rain.
"It would have been interestingly poised and there probably would have been a result in this (game).
"It's not three or four-day test match wickets, they're five-day grinding wickets which you have to work incredibly hard (on) for your fruits.
"I don't see anything wrong with them. They've been pretty good and they've certainly allowed both teams to have periods of dominance throughout the test match series so far."