The Blue Jays led 5-0 in the fourth inning Saturday and 6-2 in the seventh.
"We're a little bit shell-shocked right now," Gibbons said.
Blue Jays relievers entered play Sunday with a combined 5.35 ERA -- the second-worst in the majors -- and five blown saves in 17 opportunities this season.
Loup relieved R.A. Dickey after Clint Barmes' leadoff double in the seventh, and the Pirates tied the score on Josh Harrison's RBI double, Pedro Alvarez's run-scoring groundout and pinch-hitter Jordy Mercer's two-run double.
"You don't expect [Loup] to implode like that," Gibbons said. "I'm sure [the relief pitchers] don't want to hear that phone ring, I'll tell you that. That's the way it's been going."
One inning later, Ike Davis reached on a one-out infield single against Redmond (0-3), Harrison singled and Neil Walker hit a drive off the top of the wall in center field, scoring two runs to propel the Pirates to victory. The Pirates could have boosted their lead, but Starling Marte lined out to first against Chad Jenkins with the bases loaded.
"It's tough because it can really spiral on you," Dickey said. "That here-we-go-again syndrome can start to set in if you're not careful."
Before the game Saturday, Gibbons removed Sergio Santos from his role as interim closer after he blew three of his past four save opportunities. He said Toronto will use a closer-by-committee approach until Casey Janssen (oblique) returns from the disabled list. But Gibbons said Loup would feature prominently in that mix.
In an attempt to rejuvenate the beleaguered bullpen, the Blue Jays are planning to promote top pitching prospect Marcus Stroman from the minors prior to Sunday's game. Stroman will take the 40-man roster spot of starter Brandon Morrow, who is out indefinitely with a finger injury.
Although Stroman is a starting pitcher, Gibbons said that the right-hander will start his major-league career in the bullpen.
Toronto slugger Jose Bautista, who hit his ninth homer of the season Saturday, admitted that the loss was frustrating.
"Every loss is frustrating," Bautista said. "I don't think that we're going to start pointing fingers at anybody just because we've lost a couple games in a particular fashion."
Information from The Associated Press was used in this report.