Ross Taylor's 12th Test century, together with a quick burst of wickets in the afternoon session, gave the Black Caps hope of levelling the three-match series on day five in Dubai.
Pakistan slipped to 75-4 at one stage having been set 261, but recovered to reach stumps on 196-5.
Although his side were ultimately unable to claim victory, McCullum took heart from New Zealand's efforts and reserved particular praise for Taylor and first-innings centurion Tom Latham.
"It was a very good Test match and both teams came out with the right result," said the skipper.
"For us to win the toss and get the first opportunity with the bat was huge. We played aggressively and we played a brand of cricket to give us the opportunity to win this Test match.
"I'm really proud of the boys for their efforts. The seamers were superb on a pretty unresponsive wicket. I thought it was a great Test match and we more than played our part.
"The two centuries from our guys, I mean to travel here and execute the game plan under pretty extreme conditions, I'm delighted with the guys. We've some quality players but we've also got people who are pretty fearless.
"We'll take a lot of confidence and look forward to [the final Test in] Sharjah."