While Greatholder was trying to come to terms with a case of what-ifs, he took comfort that Bay gloveman Shaun Peta didn't do much in the first 45 minutes against the best side in the country.
It wasn't until the 52nd minute that Chad Coombes made perfect sense of an Adam Dickinson cross with his head to find the equaliser past Peta.
In the 70th minute, David Mulligan put Auckland ahead 2-1 after some Luis Corrales diligence only a minute after coming in for debutant Ivan Diaz.
Not satisfied and perhaps making the most of his time off the bench to show coach Ramon Tribuliext he belonged in the starting XI, Corrales increased the lead to 3-1 when he chipped the ball over Peta 10 minutes later.
In the 88th minute, referee Nick Waldron sent Mulligan for an early shower for a deliberate hand ball.
Bay centre-mid Tom Biss stepped up to send keeper Williams diving the wrong way from the penalty-kick spot.
Three minutes into added time, Greatholder rued his troops' inability to equalise.
"They [Auckland City] are a professional unit and they know what to do so their quality and class showed for about 20 minutes in the second half," he said.
Retrospectively, he felt the Bay's standards were much higher now and they were prepared to compete for the top-four position.
"We're always trying to get as many points as we can and, if it happens, then we could be in a great game against Team Wellington in the last game," Greatholder said as the Bay missed the opportunity to bridge the four-point gap on fourth-placed Wellington who lost 3-1 to third-placed Waitakere United yesterday at Whenuapai.
Undefeated Auckland secured the minor premiership and remain on the top rung with 32 points while Canterbury United are second on 25 points after beating Otago United 3-0.
"If we can't make the top four then we're just not good enough so the points table doesn't lie," was the frank assessment of Greatholder as the franchise seeks its first play-off in the premiership's eight-year history.
The Bay play YoungHeart Manawatu in a White Ribbon (inaugural knockout cup) match in Napier this Saturday because Auckland are off to Papua New Guinea to compete against Hekari United in the O-League.
The Bay will host Waikato United at home the next weekend then have a month off - because of the Olympic qualifiers in Taupo - before travelling to Wellington.
Tribuliext conceded yesterday it was tough when the Bay drew first blood and took to the bunker for the first half.
"It was difficult to play through them but we knew it was going to be that way so played with patience and we were lucky to come away with a win," he said.
"We're happy to have won the minor premiership but we have to keep going because we haven't really won anything yet."