However it looked as if they would be on their way to defeat after three tries in 15 second-half minutes from Michele Rizzo, Benjamin de Jager and Tobias helped put Treviso 26-23 ahead.
Morgan had other ideas to keep the Ospreys unbeaten in second in Heineken Cup Pool 5 and Johnson is keeping his fingers crossed rivals Saracens and Biarritz underestimate the Italians too.
"Maybe we're not giving enough credit to Treviso," said Johnson. "Their form has been pretty good, and it's not all that long since they put 50 points on the Newport Gwent Dragons.
"I'm hopeful that other sides will under-rate their quality. They can still have major say in the fate of this group.
"I was very disappointed with our display, and I was very disappointed with our skill set. It wasn't perfection but our destiny is still in our own hands, and that's not a bad thing."