"At the same time, they came down and got the job done - a good team goes to the lower teams and just does a job. It's not flash, it's not fancy, they just roll their sleeves up, do the job and move on to next week. They don't have to win by six or seven, they know they just have to win 1-0, 2-0."
Tauranga had what was arguably their best chance of the game in the opening minutes when a pin-point Jerahl Hughes cross was put over by Harry Gawtrey, who had been drafted into the first team from the reserves.
"I don't think he headed it, I think it came off his shoulder - he mistimed his jump altogether," said Lowry. After coming off the bench the previous weekend, Gawtrey was given a start on Sunday.
"He's been looking very, very sharp in training. Last week we brought him off the bench and he's done ever so well."
By contrast, Suburbs' second goal was a free, well-timed header by Damien Mosquera, from a textbook cross by Hayden Johns that gave City goalkeeper Tom Pamment no chance.
Lowry struggled to explain his side's position in the league, third from bottom.
"We do ever so well, but we haven't got the killer [instinct]. Sometimes I think we're so close and sometimes I think we're so far away."
A second-half talking point came when Colm Kenny not only had a penalty shot turned down, but was also booked for his efforts.
"I don't think he should be going down [in that situation]. Maybe he was pushed but I think maybe the way he's reacted doesn't help," said Lowry.
"When things are against you, it's like eating crumbs - you see all the crumbs falling off the table and we're fighting for crumbs now, whereas last year we were eating steak. People say we're doing ever so well, but we don't finish off."
Eastern Suburbs' WaiBOP Utd keeper Zac Speedy had just one potentially difficult moment in the second half, with Ray How up from his central defensive position for a corner to put pressure on Speedy, but he recovered to snuff out the danger.
This week, ahead of the visit to Hamilton Wanderers next Saturday, there will be time for reflection.
"We'll talk about it at training and have a chat about it, see what the players think. We'll have an honesty night and an open night. Sometimes we need to see what they are thinking."
There will also be a chance to assess injuries, with leftback Cameron Grieve missing Sunday's game with a groin injury and Hughes coming off midway through the second half with a bruised thigh.