But that didn't mean there wasn't Major League talent in the later rounds. It was up to Buckley and his staff to find it.
"We say that every year, and then you get Albert Pujols in the 15th round or Matt Kemp in the 16th round or Chris Heisey in the 17th round," Buckley said. "There are big leaguers up there. We just have to keep trying to find them."
Whether any were found over the past three days is the great mystery, of course. In most cases it takes three to five years for a drafted player to get into position for a Major League callup -- if it happens at all.
It's not surprising that the Reds went heavy on both college players and pitchers this year.
Of the 42 players selected by Cincinnati, 27 were pitchers. That includes first rounder Nick Travieso, a high school right-hander out of South Florida.
The Reds focused heavily on pitching in the bottom portion of the Draft. Eight of the final 10 picks on Wednesday were hurlers.
Over the past few years, the Reds have generally leaned on college talent in the Draft, but it was an even larger ratio this time, with 30 taken out of colleges. That has partly to do with new rules that limit the amount of bonus money available.
"The younger you draft, the bigger your budget has to be," Buckley said. "A college junior is giving up one year of amateur status, so you're paying for one year of college. A high school kid? It's four years of college. He's usually in better position to demand a bigger signing bonus. [Your bonus allotment] has to do directly with where you select."
When it came to position players, the Reds were looking for a certain type of hitter.
"I wanted to try and get more contact hitters," Buckley said. "Organizationally, since I've been here, strikeouts have been a problem. We tried to do address that with [compensation-round picks Jesse] Winker and [Jeff] Gelalich and other guys who were picked. It's something I've tried to address since I got here."
There were a couple of notable selections during Wednesday's later rounds. With their 30th-round selection, (No. 922 overall), Cincinnati picked Georgia Tech center fielder Kyle Wren, the son of Braves general manager Frank Wren.
"He's a good player," Buckley said. "We'll have to see. He's a sophomore-eligible player at a very good school. He needs to get a little stronger. He's not a very physical guy. He kind of wore down as his season went on."
Wren, 21, is likely to return to school, however, since he has two more years of eligibility.
"I'm happy and proud of him to be rewarded for all of his hard work," Frank Wren said. "Even though he has grown up around baseball his entire life, it is still special to see that you have been selected."
In the 32nd round, the Reds found a local product in right-hander Christian McElroy out of the University of Cincinnati. McElroy, the 982nd overall pick, hails from nearby Middletown. A 6-foot-4 redshirt sophomore, he had a 4.41 ERA this season for the Bearcats in 13 games, including nine starts.
"We'll see what happens," Buckley said. "He's kind of what we call at this point a summer draft. We'll follow him and see if we can mutually agree on something."
After the Reds' scouting department has spent weeks, months -- and, in some cases, years -- preparing for this Draft, the task now is to sign their picks. A new rule for 2012 has shortened the deadline by a month, to 5 p.m. ET on July 13.
"That's a good thing," Buckley said. "Your higher picks were all waiting until Aug. 15. Now you can tune them up for 10 days and they can play all of August. It's very important for that kid to get his first summer behind him. It's the hardest one because of wood bats, playing every day with better competition."