His team has an opportunity to be part of history following its dramatic four-run win in Abu Dhabi.
New Zealand has not beaten Pakistan in an away test series since a 1-0 victory in Lahore in 1969.
Stead said his side would need to improve if it was going to clinch a series victory.
There are two areas in which the Black Caps look vulnerable. The tail looks awfully long and really starts at No7 where all-rounder Colin de Grandhomme looks ill at ease against spin.
Leg-spinner Ish Sodhi grabbed three wickets in the test but was a little on the expensive side. Has he done enough to keep Will Somerville out of the starting XI?
It might be worth gambling on the tall right-arm off-spinner. He will certainly get more bounce than the other spinners in the New Zealand squad and Pakistan will not know much about the 34-year-old former Otago player.
But there were many more positives to emerge and Stead is likely to stick with the side which delivered in such wonderful fashion.
Ajaz Patel is certainly not going anywhere after his match-winning five for 59, Neil Wagner was at his ''lion-hearted'' best, and Henry Nicholls and BJ Watling helped set up the win with a crucial 112-run stand for the fifth wicket on day three.
''We all know the game could have gone either way but it was nice to come out on the right side of it,'' Stead said.
''I always believed we were in with a chance the way the wickets had fallen throughout the match. It is just being in that position to give ourselves a sniff at the end was all we could do.
''I guess in some ways you let the cricketing gods work out which way it will go.
''But we were accurate enough [and] we applied enough pressure that it went our way. It was great to be part of a test match like that.''
The Black Caps had to fight throughout the game after slumping to be all out for 153 on the opening day.
''My message to the boys was if [we] could lose wickets in clumps then why can't we do that to them as well through sustained pressure.''
Wagner and Patel took that to heart.
''The two of them bowled something like 24-25 overs in a row and that was just a sterling effort. I'm really, really proud of the way they went.''
''The great thing about Ajaz is he has just been calm under pressure and that is not always easy when you come into your first test match.''
Pakistan will be hurting and will have to reflect on an afternoon when there were plenty of injudicious shots played.
Stead is not expecting Pakistan to repeat those mistakes when the second test gets under way in Dubai on Saturday.
''Pakistan are a good team and they are hard to beat over here.
''That is what made [the test win] so pleasing.
''But they will be better for it. If they have taken us lightly, then they certainly won't be now.
''I expect them to better and I expect us to get better as well.''
