The 22-year-old pitching prospect, considered a longshot to open the season with the team, was sent to minor league camp on Wednesday along with left-hander Ricky Romero.
They are expected to open the season in the starting rotation with the triple-A Buffalo Bisons.
Detroit lit up Stroman for seven runs on six hits in one-third of an inning in Tuesday’s 18-4 pre-season drubbing of Toronto.
"He was kind of the odd man out," said Blue Jays manager John Gibbons. "He had trouble throwing strikes [Tuesday]. He's got to do that."
Stroman, whom the Jays drafted out of Duke University in 2012, leaves major league spring training with a 14.46 earned-run average in four appearances, including one start. He allowed 19 hits over 9 1/3 innings pitched while opposing hitters batted .432 off Stroman.
“I will do everything in my power [to make the team] but if it doesn’t work out, it doesn’t work out,” Stroman told reporters in February. “I’ll be working hard to get there [the majors] sometime this year.”
Last season, he posted a 3.30 ERA and struck out 129 batters 111 2/3 innings at double-A New Hampshire.
Toronto general manager Alex Anthopoulos has said Stroman is major-league ready but would like to see him start the season in Buffalo.
Romero, 29, started Tuesday’s contest and walked five batters while allowing three runs in 2 2/3 innings. His outing also included two wild pitches and a hit batter.
Gibbons tried to soften the blow for Romero, saying the southpaw had pitched well earlier in the spring and was moving in the right direction after two troubled seasons.
"We really like what he did this camp," Gibbons said. "Just go down there and polish it up."
Romero, a former 15-game winner with the Blue Jays, spent the bulk of last season in the minor leagues attempting to regain his once-all-star form. He wasn’t part of the team’s 40-man roster at the start of spring training last month.
Romero leaves Toronto’s camp with a 3.72 ERA in four exhibition games. While he held opposition hitters to a .200 average, he walked 10 in 9 2/3 innings. Control issues were a problem in 2013 with Romero walking 63 batters in 113 2/3 innings in 22 starts with Buffalo.
He had a 5-8 record in those outings with a 5.78 ERA. In four games (two starts) with the Blue Jays, he was 0-2 with an 11.05 ERA, walking eight in 7 1/3 innings.
Gibbons said Romero needs to do "whatever it takes" to throw strikes.
'A long road'
In 2011, Romero went 15-11 with a 2.92 ERA with Toronto but sported 9-14, 5.77 totals the following campaign.
"It's a long road. You never know if a guy's going to make it back from that or not," said Gibbons. "But he was starting to show the signs of it. [Tuesday] he wasn't as good and it just kind of reaffirmed, 'Hey start him down there, but he's moving in the right direction."'
Romero had been a feel-good story earlier in spring training.
Gibbons called him "the big talk of camp" last week after giving up one run in seven innings for an ERA of 1.29 in three appearances. But Romero fell back to earth Tuesday in Lakeland.
"We've taken too many steps forward to dwell on this," Romero said philosophically afterwards.
Brandon Morrow has been named the Blue Jays’ fifth starter to begin the season while Drew Hutchison is also expected to be part of a starting rotation that includes R.A. Dickey and Mark Buehrle.
Left-hander J.A. Happ, who is attempting to win the final spot, starts Wednesday against his former club, the Philadelphia Phillies, at 1 p.m. ET.
In other Blue Jays news, Gibbons said closer Casey Janssen felt "great" after a throwing on the mound Tuesday and will go again Friday. He's slated to make three or four appearances before the season starts March 31 in Tampa.
Janssen has been limited in action to protect against shoulder soreness.