Medvedev came into Sunday's final having won titles in Rotterdam, Doha and Dubai but was thrashed 6-3 6-2 by Spaniard Alcaraz, leaving him one victory short of matching his 20-match winning run that ended in early 2021.
"Damn, one away from my record. That's actually disappointing," Medvedev said. "This would be cool to try to beat it and maybe try to prolong it as long as possible. It's great to have these streaks.
"Really disappointed it ended, but a lot of confidence from this streak. Last year, that's what I was missing. I was doing sometimes finals, semis in Cincinnati, playing good but not playing well enough in the semis.
"I managed to win 19 matches in a row. I'm proud of it, and now it's time to try to build a new streak. There's no other way in tennis."
Medvedev said he was looking forward to the claycourt season that follows this week's Miami Open, despite not being a big fan of the surface.
"Sliding is something that's not easy for me on claycourts," Medvedev said.
"But I made some good results in the past on claycourts in big tournaments. I'm feeling great right now at this part of the season, mentally and physically.
"So I'm looking forward to the clay season but first I want to try to do well in Miami, where it's still hardcourts even if maybe it'll be very slow."
