The 31-year-old right-handed swingman was hit for seven runs on seven hits, including a home run, in two-thirds of an inning of relief in the Blue Jays' 10-3 loss to the Rays.
That raised Estrada's ERA for the spring to 15.43.
"He got hit around pretty good," acknowledged manager John Gibbons. "That happens sometimes. There's no reason for it."
Estrada and youngsters Aaron Sanchez, who was a leading candidate to be the Blue Jays' closer this season, and Daniel Norris are now battling for the two spots in the starting rotation behind R.A. Dickey, Mark Buehrle and Drew Hutchison.
"I don't think we can replace him [Stroman] totally, but hopefully we can hold the fort down a little bit," Gibbons said.
"We've got more depth, more quality depth, than we've had, in the past couple of years anyway. That kind of softens the blow a little bit."
Gibbons said the fact that Estrada can start or come out of the bullpen enhances his value.
"The other two guys [Sanchez and Norris] are big-time power guys. He's not that way," Gibbons pointed out. "It would probably be easier for him going from the bullpen to the rotation."
Estrada would give the Blue Jays a veteran presence in a bullpen that figures to otherwise be quite young.
With the Milwaukee Brewers, Estrada averaged more than 20 starts over the past three seasons.
A year ago, Estrada struck out 127 batters in 150 2/3 innings in 18 starts, in addition to making 21 relief appearances.
Estrada also served up 29 home runs last year, the most among all Major League starters.
Estrada's mind-set remains the same as it was before Stroman suffered his season-ending knee injury.
"I'm here to make outs, and whatever decisions need to be made, that's up to [management]," said Estrada. "I'll do whatever it takes, bullpen or start, to make this team. I just want to help them win games."