"I know I have to keep working hard and just be patient ... like we were before that try," Apikotoa added.
Magpies head coach Mark Ozich and his assistant Josh Syms, a first-time combination at this level, had every right to be elated.
"I couldn't be happier with the way the boys hung in there. You can't fake a team's togetherness and these boys are doing everything we are trying to build. Look at the impact our young boys delivered off the bench," Ozich said.
Syms was quick to point out the hosts were without captain Ash Dixon for the entire match, captain for the day Gareth Evans and lock Michael Allardice for the second half.
Nineteen-year-old hooker Kianu Kereru-Symes who replaced the injured Ben Power in the 28th minute, Baby Blacks loosie Will Tremain, who replaced Evans at halftime, lock Geoff Cridge who replaced Michael Allardice at halftime, Apikotoa and second five-eighth Pasqualle Dunn all impressed with their impact.
Kereru-Symes made eight carries and 11 tackles. Tremain forced a turnover with his first involvement, made three tackles, had an average gain of 4.5m with his four carries and beat one defender with his one line break, Cridge made seven tackles and had an average gain of 1.9m from his nine carries, Apikotoa made seven carries and three tackles during his 26 minutes of action and Dunn had an average gain of 9m from his three carries.
Ozich confirmed Dixon will miss the remainder of the season with his knee injury.
Evans collected an eye injury but should be available for Thursday night's Ranfurly Shield Challenge against Waikato in Hamilton, Power collected a sprig to his hand and a decision on his availability won't be made until after scans are done and Allardice was suffering from a virus which forced him from the field.
Magpies halfback Brad Weber deserved his player-of-the-match award but only just ahead of Steamers first five-eighth Mike Delaney.
Weber scored two tries and had an average gain of 9.5m off six carries. He beat three defenders during his two line breaks and while he made five tackles he missed three.
Weber, who took over the captaincy in the second half, was impressed with the manner in which his troops came out of the changing shed in the second half.
"But we let them come back into it. We just needed to work hard and chop tackle more. We did that and our Magpies bench showed us the way," Weber said.
While the Magpies deserve praise for holding the top perch on the table there is still plenty of room for improvement.
Once again they missed too many tackles, 24, conceded too many turnovers, 17, and kicked too much possession away.
The Magpies scrum was nowhere near as good as it was the previous week.
Tighthead prop Ross Glendenhuys was a powerful scrummager in the Steamers pack.
As expected, Steamers flankers Mitch Karpik and Tanerau Latimer were workaholics on defence with 15 and 11 respectively.
Steamers halfback Richard Judd matched Weber's two tries. He had an average gain of 9m off his seven carries and beat four defenders.
Former Magpies outside back Matt Garland had an average gain of 10m off nine carries and beat three defenders.
Match highlights:
Heartstopper: When Steamers No 8 Hoani Matenga's shoulder connected with the eye of Magpies captain and No 8 Gareth Evans in the 24th minute. This created another injury concern for the Magpies.
Turning point: When Magpies prop Joe Apitokoa scored in the 78th minute and Tiaan Falcon slotted the conversion to secure the win. This nailbiter could have gone either way until then.
Man of the match: Magpies halfback Brad Weber. Two crucial tries, three defenders beaten, an average gain of 9.5 metres off six carries and five tackles. Steamers pivot Mike Delaney was close behind Weber.
Scorers:
Hawke's Bay Magpies 29 (Brad Weber 2 Jonah Lowe, Joe Apikotoa tries; Tiaan Falcon 3 cons, pen), Bay of Plenty Steamers 28 (Richard Judd 2, Mike Delaney tries; Delaney 3 pens, 2 cons). HT: Steamers 13-8.