The fourth-seeded Argentinian was the first player this week to cope with Isner's big serve, breaking the American twice in the opening set and once in the third.
He also had nine break points in the second set but could not convert.
Monaco told www.atptour.com: "The first set, I played really well, and then he came back in the second set.
"In the final set, it was a battle. We fought until the last point.
"I served pretty well in the last game, so I'm happy for that."
He added: "This is a great moment in my career. I've worked very hard to be here. I have the clay-court season in Europe now, which is very important for me. This tournament is going to bring me a lot of confidence."
Isner blamed a poor start for the defeat.
"I came out of the gates slow," he said. "I wasn't quite there.
"It took a while to get warmed up and engaged in the match. I got better as the match went on."
He added: "All in all, it was a good effort and was the best match I played all week. That's encouraging."