Things didn't start off well from the start with some poor defending leading to Thorner going 2-0 up after less than half an hour.
Leeds managed to claw one back just before the break through Charles Myers after the only good spell of football that Maccabi enjoyed in the whole match.
Not sooner had the second half started, Thorner added a third goal which was then quickly followed by a fourth.
From then on, it was the home team who had the bit between their teeth and the confidence to attack a shell-shocked Maccabi at will, who had by now lost their confidence and shape.
Tim Zoltie scored a consolation goal with five minutes to go with the final score ending 7-2.
Leeds Maccabi manager Simon Marks said: "On paper, we had a strong team capable of progressing quite far in this Cup, but unfortunately, we play on grass not paper and it was a poor performance all round.
"Losing two players on the day was a blow and we paid the price for maybe being too complacent given our recent performances. We lacked options in many areas today, but didn't do ourselves any favours with some poor defending."