(CNN) — Former tennis star James Blake’s run-in with New York police — in which an officer blindsided him, threw him down on a Manhattan sidewalk, then pulled him up in handcuffs — lasted all of 10 to 15 minutes. A difficult time, no doubt, but nonetheless a limited one.

On Monday, he expressed hopes that the aftermath of that ordeal would last much longer.

Blake talked to reporters after meeting with New York Mayor Bill de Blasio and police Commissioner William Bratton not just about that incident earlier this month, but about what the city and police department generally can do to prevent the same thing from happening to others.

“We’re not looking for a quick lawsuit, we’re not looking for anything that’s going to be a quick and easy solution,” he said. “We’re looking for a lasting, positive impact on the city and on the police force.”

What specific changes might come out of this? Blake didn’t offer details, nor did city officials.

“Right now, we still just have pretty broad strokes but on a similar page,” Blake said. “… The process will sort itself out very quickly … I’m confident of that.”

Blake: ‘Trying to react in a positive manner’

Once ranked No. 4 in the world, Blake was staying in the Hyatt Hotel in Manhattan on September 9 — while the U.S. Open, across town, was in full swing — waiting outside for a car to pick him up to take him to the tournament.

That’s when, a surveillance video shows, plainclothes police Officer James Frascatore swoops in.

In the brief time he was detained, Blake has told CNN that neither Frascatore nor other officers present identified themselves as law enforcement or displayed their badges.

Two law enforcement sources later said that investigators looking into the purchase of cell phones using fraudulent credit cards had set up a sting operation at the hotel. The male suspect that they were actually looking for was later taken into custody.

Blake went public with his story to a number of news organizations, and New York authorities never denied his version of events. In fact, De Blasio and Bratton to called to apologize before Monday’s meeting.

Not every innocent person who gets taken down and detained by authorities gets such apologies, much less a face-to-face meeting with a mayor and top law enforcement official.

While noting “the video … is pretty compelling evidence by itself,” Blake acknowledged that his celebrity has played a role in his treatment since the incident. And now, he says, he wants to make the most of it.

“Life is 10% what happens to you and 90% how you react to it,” he said. “So I’m going to try to react to it in a positive manner and make a difference for all those that may not … be in the same situation.”

CNN’s Sarah Jorgensen contributed to this report.