Corporate jet Captain reported being issued an ATC clearance on landing rollout to exit at a specific taxiway; which the aircraft was unable to slow to taxi speed and then cleared the runway at the next taxiway. The late clearance to exit the runway at the taxiway; resulted in the aircraft on final approach being directed by ATC to go around.

Narrative

We landed on runway 1L at LAS at XA13. We were following an air carrier on final and Airrcraft Y behind us. We were given 170 KTS till '4-5 mile final' from approach which we complied with; to the 4 mile final.We followed the glide slope on the ILS to touch down zone. (In visual conditions). Over the numbers; we experienced a slight tailwind and light turbulence that caused a longer landing roll out.Abeam N taxi way; we were asked to vacate N. We were still slowing and at this point we were already passing N and we were not at a safe taxi speed for the 90 degree turn. Then the tower asked us to vacate high speed M taxiway to the right. We came to a safe taxi speed for the right turn (slightly passed the leading lines for high speed exit) but before we could commence the 90 degree right turn; we were instructed to make a left turn on J which we did. Aircraft Y behind us was asked to go around between the instructions to vacate N and then later to vacate M. (at least that is to the best of my recollection).While still vacating the runway; we were advised of our possible deviation. We asked tower to standby as we were busy going thru our flow and figuring out where the FBO wanted us to go. Once parked on the ramp and passengers were gone; I attempted to contact the tower at XA28 but no one picked up and went to some answering device. I then called back at XA29 and a controller answered the phone.I inquired as to what the issue was. I had to ask 3-4 times before the controller finally told me that we should have vacated on taxiway M; which we were trying to do.From what I gather; the issue was the go around with Aircraft Y. I am not sure what the spacing looked like but we had to slow to a safe taxi speed to be able to vacate the runway either to the left or the right. It would have been helpful if tower would have communicated their expectation and/or request for vacating the runway before we actually land so we could have briefed it in advance and made every effort to safely accommodate their request.Also important to note that while on final; tower asked Aircraft Y (assuming the one behind us) if they could accept runway 1R which they did not. Based on that; I would assume that there were concerns with the spacing in advance of us landing. Again we did everything we could to help but we did not deviate from anything. Safety first and there was no way we could have taken taxiway N.