The Welsh region needed a late penalty strike from young replacement Matthew Morgan in order to avoid a shock defeat to the Italians, who led the try count thanks to efforts from Michele Rizzo, Benjamin de Jager and Tobias Botes.
The hard-earned 26-26 draw leaves the Ospreys undefeated and sitting in second place in the pool after the opening two rounds, but Johnson knows they will have to pick up the pace next month.
"I'm very disappointed with our display, and I'm very disappointed with our skill set," he lamented after the game.
"Did we want four or five points? Yes of course we did. But will I settle for two? Well I'll certainly settle for two before one, or even none.
"It wasn't perfection but our destiny is still in our own hands, and that's not a bad thing."
The Ospreys were poor overall, though they did manage to cross the Treviso whitewash twice, courtesy of Tommy Bowe and then Ryan Jones.
But the visitors found themselves playing catch-up for most of the second half as Treviso registered three tries in a 17-minute spell, with winger de Jager's magnificent solo effort the best of the lot.
In the end, it was a game that Treviso should really have won, a point not lost on their coach Franco Smith.
"After our performance last week against Saracens, I was really worried about this game and I can't believe I'm unhappy with a draw," he said bluntly.
"It was definitely two points lost rather than two points gained. We had a chance today to win this game, but we threw it away."
Treviso remain rooted to the bottom of the pool but Johnson, for one, is confident that the Italian club will still have a major part to play in deciding who progresses to the quarter-finals.
"Maybe we're not giving enough credit to Treviso," he admitted.
"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."