Cueto surrendered Anthony Rizzo's 30th homer during a wet first inning, and the Reds went on to a 3-0 loss to the Chicago Cubs on Tuesday night.
"I was upset," he said with catcher Brayan Pena serving as his interpreter. "They knew it was going to rain. They should've called timeout and not started the game. I was afraid I was going to hit him with a pitch. I couldn't grip the ball."
Starlin Castro, in his first game back from the bereavement list, followed with a single as the rain increased, forcing a 50-minute delay just five minutes into the game.
Arismendy Alcantara added a two-run shot in the seventh for the Cubs, who have won four in a row for the first time since June 30-July 4.
"The pitch was high and out of the zone," Cueto said. "I think it was a hit and run. If he didn't have to swing he wouldn't have."
Travis Wood pitched six innings of two-hit ball against his former team for his first win in two months.
"I thought both pitchers handled the rain delay very well," Reds manager Bryan Price said. "Here in the Midwest you have to expect those popup showers. There is nothing you can do about it. Woody commanded both sides of the plate with his cutter. He didn't give us anything good to hit."
Cincinnati was shut out for the 12th time this season. Cueto (15-8) struck out eight in 6 1-3 innings in his second straight loss after winning seven consecutive decisions.
Wood (8-11) struck out five and walked one in his first victory since he pitched eight innings in a 3-0 win at Philadelphia on June 15. The left-hander, who made the All-Star team last season, was 0-6 with a 5.45 ERA in his previous 12 starts.
He improved to 2-5 with a 3.30 ERA in nine career starts against the Reds, who selected him in the second round of the 2005 draft.
Rizzo went deep with two out in the first, driving a 2-1 pitch into the seats in right. The All-Star first baseman joined Miami's Giancarlo Stanton as the only two National Leaguers with at least 30 home runs.
Alcantara followed Matt Szczur's leadoff single in the seventh with his fifth homer of the season and second in two games. He also homered on Sunday against Baltimore in Chicago's final home game before embarking on a seven-game, six-day road trip.
Cubs: RHP Jacob Turner makes his first start for Chicago after two relief appearances since being acquired from Miami on Aug. 8.
Reds: RHP and new father Mat Latos, hurt by blown saves in two of his last three starts, makes his second start of the season against Chicago.
The Cubs have hit at least one home run in 10 consecutive games for their longest such stretch since a 10-game run from Aug. 2 through Aug. 12, 2011.
RHP Daniel Corcino celebrated his 24th birthday by making his major league debut, pitching the ninth for Cincinnati. He was recalled from Double-A Pensacola on Friday.