The Royals prospect carried a no-hitter into the seventh inning before allowing an RBI double as the Wilmington Blue Rocks were blanked by the Kinston Indians, 1-0.
Marks (2-3) got himself in trouble by walking Jeremie Tice with two outs in the seventh. Adam Abraham followed with a two-strike double down the left-field line but was thrown out at third after Tice crossed the plate with the game's lone run.
"It was supposed to be in the dirt and I thought it was going to be a swing and a miss, but I left it in the zone and he got the best of it," Marks said of Abraham's double.
A 2009 third-round Draft pick, Marks settled for his Carolina League-leading second complete game. He walked two and struck out seven in his best start at the Class A Advanced level.
"At the moment, very frustrating. Probably the maddest I've been with myself all season," the University of Louisville product admitted. "To get two strikes and not be able to put him away like that and make that sort of mistake. ... Looking back on the game, I take it for what it's worth -- we got shut out, they got one run, there's not much I can do about it. That's just part of the game."
The 23-year-old left-hander is 1-1 in his last three starts, despite allowing only two runs and striking out 20 while walking four over 19 innings.
"I think all four pitches were working," Marks said. "I finally started getting my changeup in the zone. Early on, the slider helped me out and my fastball really helped get me strikes.
"I didn't really throw [my curveball] as much as I should have, but it's hard to mix in things when you're throwing so well. It was around the zone and it got me a couple of strikes, but it wasn't as important as the other pitches."
The Royals acquired Marks along with right-hander Vin Mazzaro last November in the trade that sent outfielder David DeJesus to Oakland. He has a 4.80 ERA in 10 games, including six starts, in his first season in the Kansas City organization.
"I can't really say that it's the reason why I had some terrible starts," Marks said, "but I think that change really does affect you. It just has to do with getting comfortable on the mound and getting used to a new catcher."
Giovanni Soto was nearly as good for the Indians, equaling his career high with 10 strikeouts and limiting the Blue Rocks to two hits over six shutout innings.
Jose Flores (2-3) fanned four and allowed a hit over 1 2/3 frames for the win and Preston Guilmet notched his league-leading 12th save by retiring the final four batters in order.