Westpac economists said they had expected the June quarter to mark the high point for growth this year, given the one-off boost from tourism and a rebound in agriculture and transport from previous weak quarters.
"In that light, a 0.8 per cent quarterly rise is not that impressive," they said in a commentary.
Westpac has recently revised its September quarter growth forecast down to 0.7 per cent, and over the next year as a whole it expects GDP growth to fall "significantly short of Treasury and Reserve Bank forecasts".
ANZ said the June quarter improvement, coupled with the small upward revision to the first quarter, made for a slightly better picture overall.
"However, we'd still class it as somewhat of a 'middling' result," ANZ economists said.
"It is clear that the economy is grappling with some meaningful headwinds, which look unlikely to dissipate," the bank said.
"That presents a challenge for the Reserve Bank in generating above-trend growth - and hence higher inflation - and reinforces that the official cash rate (OCR) is not heading higher any time soon."
The Reserve Bank kept its rate at 1.75 per cent in August and said its policy would remain accommodative "for a considerable period".
The consumers price index did not move in the June quarter, and rose by just 1.7 per
cent in the June year.
"The Reserve Bank faces a challenge," ANZ said. "Putting aside the fact that today's 'middling' result actually raises questions about the economy's growth potential at a time of anaemic productivity growth, growth barely at trend is hardly going to lift core inflation in a meaningful way."
ANZ said growth, combined with forward indicators pointing to a further turn south in some parts of the economy, such as housing and construction, reinforced the likelihood that the OCR would not head higher any time soon.
In its commentary, ASB said GDP growth has been "underwhelming" over the past year and that the June quarter rebound had been relatively muted.
Per capita growth of 0.3 per cent quarter on quarter follows flat per capita growth in the previous quarter.
Economic growth needs to pick up on a sustained basis in order for the Reserve Bank to be confident domestic inflation pressures will return to target.
As expected, growth was led by a strong recovery in transport and increased visitor spending from hosting the Lions Tour and World Masters Games.
However, growth was capped by weak outcomes in construction, house sales, mining and non-primary manufacturing.