"We're not cutting payroll whatsoever," Dombrowski said.
Dombrowski said he's not surprised at least some Tigers fans weren't happy when the trade was announced because the team traded the "known for the unknown."
"People in general don't like those type of moves," he said.
The 25-year-old Lombardozzi hit .259 with two homers and 22 RBIs in 118 games for the Nationals last season. The switch-hitter played 48 games at second base, 23 in left field and four at third base in 2013. He will replace Ramon Santiago on Detroit's roster.
"This was not an easy trade for [the Nationals] to make, either," Dombrowski said.
Krol made his major league debut in June for the Nationals after they acquired him from Oakland. The 22-year-old lefty was 2-1 with a 3.95 ERA in 32 games with Washington.
The 22-year-old Ray was 6-3 with a 3.11 ERA for Class A Potomac and was 5-2 with a 3.72 ERA for Double-A Harrisburg, giving the Tigers a pitcher they think will start the season at Triple-A Toledo with the ability to possibly pitch in the majors if needed in 2014. Baseball America rated him as the Nationals' No. 5 prospect.
"We are excited to be adding three solid players to the organization," Dombrowski said in a statement. "Robbie is a premium pitching prospect, Ian adds a quality left-handed young arm for the bullpen and Steve provides our ballclub with versatility in several roles as a switch-hitting utility man."
Information from ESPN's Jayson Stark and The Associated Press was used in this report.