Alan Forsyth's double means the Scots will face Austria after finishing third in a pool topped by Ireland.
"It was an ugly win," Derek Forsyth told Scottish Hockey.
"It's a game we'll learn from, but we'll need to raise our standards up to where they were in our previous games if we want to progress."
Wales face Italy, Ireland play Poland, while France take on Ukraine in Thursday's quarter-finals.
France topped their pool by beating Wales 1-0, while Ireland finished top of the other pool after Matthew Nelson's goal secured a 1-0 win over Italy.
Ireland started their campaign off with a 9-2 hammering of Ukraine following by a shoot-out win over Austria after a 1-1 draw.
The Scots had lost 3-1 to France and also suffered a penalty shoot-out defeat after a 2-2 draw with Wales before beating the Poles.
They now face an Austrian side who beat Italy on penalties after a 1-1 draw, lost that shootout with Ireland then beat Ukraine 4-2 in their pool.
"In the end, we won the match without playing as well as we know we can, so that's pleasing," said Forsyth ahead of Thursday's quarter-final.
"But we'll look to improve on this performance."
Alan Forsyth opened the scoring for the Scots against the Poles after only two minutes.
The Poles, who had lost 3-1 to both Wales and France, were denied by good saves from David Forrester before Dominic Kotulski equalised after half-time.
As the Poles pressed for a winner, Forsyth secured a victory with a solo goal.
Scotland head coach Derek Forsyth has demanding improvement despite his side finishing the World League 2 pool stage by beating Poland 2-1 in Belfast.