Manly interchange forward Addin Fonua-Blake then spilled the ball off the kick-off to hand the Warriors an attacking scrum, but the home side failed to capitalise when Johnson rushed another shot at a field goal on just the third tackle, only to see it drift wide to the right of the posts.
Manly got one more set in possession but Cherry-Evans sprayed another shot to the left of the uprights to ensure the match went into extra time.
Soon after the resumption the Warriors blew another chance to set up for a one-pointer, after a strong run from David Fusitu'a helped put them within kicking range, when an ill-conceived backline shift saw Maumalo bundled into touch.
On their next opportunity, Cherry-Evans proved the match-winner for Manly, when he banged over his second field goal, this time off his left boot.
Tuivasa-Sheck agreed with Warriors coach Stephen Kearney in saying they had lacked "football awareness" on several occasions throughout the crucial dying stages.
"Shaun felt like he was in a good position and he had a crack at it and when he missed it we all felt pretty calm about it," said Tuivasa-Sheck.
"We actually did get the opportunity to go again with David Fusitu'a's carry and we got back down the right end, but like Mooks (Kearney) was saying, just our football sense, we didn't make our way back to the middle.
"I messed up with the (offside) penalty by chasing and that gave them the opportunity to come back at us so that was disappointing.
"But I felt calm when Shaun kicked that field goal, we just needed to execute from there on and we couldn't."
The result was the Warriors eighth-straight loss, equalling their worst season record (2012 and 2015) for consecutive defeats. They are now in danger of breaking new ground with one game remaining in the regular season against Wests Tigers in Sydney on Sunday.
Despite the loss Tuivasa-Sheck was buoyed by his side's much-improved defence, having kept Manly to three tries after conceding 36 points in their last two losses to Canberra and South Sydney.
"We had a really good week prior to the game and we spoke a lot about our defence and we gave individuals one work-on and that was our defence on our goal line and it showed," he said.
"That's something that hopefully next week we can make it our standard to be that good on our try line because I know we've got it in us."