The hosts kept themselves in contention throughout the game on Friday and at one stage even threatened to make a comeback, but the Hurricanes defence held its ground.
"We didn't play a good game," Strauss said after their fourth loss in 11 Vodacom Super Rugby matches this season.
"We started the second half playing very lateral. We shifted the ball from side to side, which did not help our cause.
"We didn't stay in our structures and tried to play in the wrong areas."
Lying second in the SA conference standings, after a bye last week, Strauss said his side would need to find their feet again in an effort to close in leaders the Bulls.
"I won't say that the loss is a result of the bye or the week off," Strauss said.
Can be fixed
"We just lost our rhythm. Luckily it is something that can be fixed.
"Come Monday we will have to make the step up for next week's home game."
The Cheetahs host the high-flying Reds, who are second in the Australian conference after a 32-17 victory over the Sharks on Friday, at Free State Stadium in the next round of matches.
"We are looking forward to the game against the Reds," Strauss said.
"But we know that we have to rectify what went wrong. The Reds are a tough side that won't be beaten easily."
The Hurricanes, under pressure to perform after they were thumped by the Bulls last week, were more physical in most aspects and eventually beat the hosts at their own game.
A physical side
"We knew that we had to play an attacking brand of rugby and that we had to be very physical in our approach if we were to beat the Cheetahs at home," said Hurricanes captain Victor Vito, acting as stand-in skipper for the injured Conrad Smith.
"They are a very physical side and we had to match them in that aspect."
Scoring four tries on the day, the tourists launched themselves back into contention for a place in the knockout stages.
"I'm a bit more cheerful after getting the win," said Vito.
"After the Bulls game we knew we had to focus on playing the patterns we practised and in the end that rewarded us with a much needed five points.
"We played a physical game and that paid off in the end." – Sapa