CHICAGO -- Jose Abreu and the Chicago White Sox are delighted with the first baseman's dual selection as American League Player and Rookie of the Month for April on Monday.

However, all parties are realistic enough to know that great times can quickly turn in baseball.

"There will be some inevitable setbacks, there's going to be some adjustments," White Sox general manager Rick Hahn said Monday before his team beat the Chicago Cubs 3-1 in 12 innings at Wrigley Field. "We've already seen him go through one mini-slump, but I think it's a great testament to him on how hard he's worked and how quickly he's been able to make the adjustment to a new league and a new clubhouse and a new culture.

"It's been very impressive to watch."

Abreu became the first American League player to receive both honors in his first month in the major leagues. The only National League player to do so was Los Angeles Dodgers outfielder Yasiel Puig last June.

Abreu, a 29-year-old from Cienfuegos, Cuba, hit .270 with eight doubles, a triple, 10 home runs, 32 RBIs and 20 runs over 29 games in March/April. He topped the major leagues in homers, RBI, total bases (32) and extra-base hits (19).

No player in major league history hit as many homers before May 1 in his debut season than Abreu's total. Abreu's 10 homers set a White Sox rookie record for any month.

Abreu approached his first month in the majors with a calm demeanor.

"Maybe not nervous," he said through a translator prior to Monday's game, in which he went 0-for-2 with a sacrifice fly and a walk. "(But) I had a little anxiety of getting to know the baseball here in the United States."

Abreu was the ninth White Sox player to be named Player of the Month and fourth to win Rookie of the Month.

"There's things he going to learn that are going to make him better," White Sox manager Robin Ventura said. "I think he's going to learn in certain situations that people are going to pitch around him. Right now he's ultra-aggressive and wanting to come through and knock guys in. ... Eventually he'll be more selective and not swing at as many pitches."