After finding out the star shortstop likely will be sidelined until the All-Star break, Dickey allowed one run and five hits in 6 1-3 innings Saturday night in the Blue Jays' 3-2 win over the Kansas City Royals.
Reyes is likely out for three months with a severe left ankle sprain, an injury sustained stealing a base on Friday night.
"It certainly hurts to lose a player of Jose's calibre and personality," Dickey said. "I think it also provides us with an opportunity to come together and collectively shoulder the burden that we will miss with his absence. Sometimes a situation like that can really cause a team to jell."
Jose Bautista hit a two-run homer off James Shields (1-2), who pitched a two-hitter with six strikeouts and three walks and was the hard-luck loser.
Reyes was hitting .395 and led the majors with five stolen bases before the injury.
"We're going to go as far as the rotation is going to bring us," Blue Jays general manager Alex Anthopoulos said. "That's really what it comes down. It starts there. No question, Reyes is a big loss offensively, but I do think we have enough depth from our offensive standpoint to be fine. We just need to get the rotation going."
Coming in, Toronto's revamped rotation had a 7.55 ERA and J.A. Happ (2-4) was the only Blue Jays starter to win.
"Nobody has been happy with the way things have gone, not as a starting staff," Dickey said. "We all talk about it. It's obvious we haven't performed, not only the expectations, but our ability. And we all feel very responsible to that. That being said, nobody in here is panicking and nobody in here is trying any less hard than normal. "If we just keep eating up innings, keep looking to get better, improving, growing, we're going to be fine."
Acquired from the New York Mets after going 20-6 last season and winning the NL Cy Young Award, Dickey was 0-2 with an 8.44 ERA in his first two starts for Toronto. Against the Royals, the knuckleballer struck out four, walked two and hit a batter, throwing 64 of 100 pitches for strikes.
"We never could muster a consistent attack against Dickey," Royals manager Ned Yost said. "His knuckler was really dancing. We never could get any consistent momentum."
Jarrod Dyson chased Dickey with a two-out double in the seventh. After Darren Oliver relieved, Dyson stole third and scored on Chris Getz's bunt single.
Casey Janssen pitched the ninth for his third save in as many chances, allowing a two-out single to Getz, who took second on defensive indifference and scored on Alex Gordon's single. Alex Escobar followed with a game-ending flyout.
"It got a little hairy at the end, but Janssen got it done," Blue Jays manager John Gibbons said. "You don't win too many games when you get two hits, but homers win."
Toronto went ahead when Macier Izturis doubled leading off the third, advanced on Henry Blanco's groundout and scored a sacrifice fly by Munenori Kawasaki, called up from the minors after Reyes severely sprained his left ankle on an awkward slide.
Kawasaki walked leading off the sixth and scored on Bautista's third home run of the season, a two-out drive. Kawasaki, who batted ninth and played shortstop, hit .295 in six seasons with Fukuoka in Japan's Pacific League, but just .192 with a .202 slugging percentage with one extra-base hit in 104 at-bats last season with Seattle.
Toronto mustered just enough to defeat Shields.
"He pitched a great ballgame," Yost said. "He threw 115 pitches and if he had to take any one back it would be the curveball to Bautista. Bautista's a strong guy and he got it out. The one pitch made the difference."
NOTES: Royals 1B Eric Hosmer has tightness in his right quadriceps and did not start for the second straight night. ... Emilo Bonifacio, who started eight games at second base and batted ninth in eight games, played right field for the first time since Sept. 15, 2011, and batted leadoff. Bautista started at third base for the first time since Aug. 4, 2011. ... Royals 3B Mike Moustakas is hitless in 13 at-bats, dropping his average to .158.