Tomi Juric gave Australia a 2-1 lead with his goal about 20 minutes from full-time, but a late equaliser from Nassir al-Shamrani crushed the visitors' hopes.
"I don't think we're going to be too happy with ourselves when we analyse that game," Sainsbury told Fox Sports.
"We conceded in the first 10 minutes, we didn't counteract that pressure that was coming from their forward line.
"To concede that late as well after working so hard to get ahead it hurts," he added.
"It almost feels like a loss because I think we deserved to win that game and take three points with us."
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| Trent Sainsbury runs against Iraq |
Saudi Arabia is tied with the Socceroos on seven points, as both teams have two wins and a draw through the first three games of round two.
"Seven points from three games is nice but nine points would be a whole lot better," Sainsbury said.
"There are a lot of positives to take away from the game but disappointment is what the boys are feeling right now."
Socceroos coach Ange Postecoglou applauded his team's effort to fight back into the contest, but agreed that they left three points on the table.
"We lost our composure a couple of times and they came into it as well. They had their moments — big crowd behind them and they were giving it everything, but you just feel we could've got more out of it."
The Socceroos' next opponent, Japan, sits third in the group with six points after a shock loss to United Arab Emirates was followed by wins over Thailand and Iraq.
The four-time Asian champions will travel to Melbourne to face off against the Socceroos at Docklands on Tuesday night.
Read more on site http://www.abc.net.au/news/2016-10-07/socceroos-draw-against-saudi-arabia-almost-feels-like-a-loss/7912108