Time will tell whether the Yankees got what they paid for when they traded Aroldis Chapman to the Cubs and Andrew Miller to the Indians in July with an eye on prospects for the future.

But in the short term, the man who let them go, Yankees general manager Brian Cashman, could not help but marvel at what the two relief pitchers gave their new teams up to and including the World Series.

Chapman blew a save for the Cubs in Game 7 while operating under a heavier-than-usual workload, but he ended up the winning pitcher when they scored twice in the top of the 10th inning and held on for an 8-7 victory.

“Aroldis Chapman and Andrew Miller, they gave everything they had and then some,” Cashman said Thursday before being honored with a Lifetime Achievement Award at The ALS Association Greater New York Chapter’s Lou Gehrig Sports Awards Benefit in Manhattan.

“They went above and beyond, obviously, on behalf of their teams. That’s a big reason why their teams were where they were and they were all playing in Game 7. Very special, talented individuals that obviously earned the right to have a lot of accolades thrown their way, to be performing under that type of pressure. It’s pretty impressive.

“That’s why the Chicago Cubs stepped up and that’s why the Cleveland Indians stepped up at the trade deadline when we thought we had to do what we did, to give up the present to have a better future.

advertisement | advertise on newsday

“We have to wait on that from our end and wait for our future to be delivered down the line. But they certainly got what they bargained for in the present. It was an epic world champion effort by the Cubs and the Indians, although I wish we were in there fighting it out ourselves.”

Cashman did not directly address whether he would like to re-sign Chapman as a free agent for 2017, other than to acknowledge the Yankees’ top offseason priority is “pitching, pitching, pitching.”

Miller, who also took on an unusually heavy workload in October, struggled in World Series Game 7 but wound up allowing three runs and striking out 30 in 19 1⁄3 innings in the postseason. He was named the Most Valuable Player in the American League Championship Series. He had a 4-0 record and 1.55 ERA for the Indians during the regular season, striking out 46 in 29 innings. The Yankees acquired top outfield prospect Clint Frazier and pitchers Justus Sheffield, Ben Heller and J.P. Feyereisen in the Miller trade.

Chapman picked up four saves and struck out 21 in 15 2⁄3 innings in the postseason. The Yankees acquired reliever Adam Warren, top shortstop prospect Gleyber Torres and outfielders Billy McKinney and Rashad Crawford in the Chapman trade.