Russia's Medvedev, a former world number one now back on the rise and ranked 11th, beat Alcaraz 6-3, 7-6 (3), handed the Spaniard his first defeat of the season after 16 wins.
But the 22-year-old, who followed up his Australian Open triumph with a title in Qatar said the streak was the last thing on his mind.
"I'm not thinking about it at all," Alcaraz said, reiterating that his biggest challenge these days is the fact that every opponent he faces seems to lift his game for the occasion.
After dropping a first-set tiebreaker on the way to a victory over 28th-ranked Arthur Rinderknech on Monday, Alcaraz quipped that he felt like he was playing Roger Federer in every match.
"Sometimes (it) just feels they're playing an insane level," he said of those trying to knock him off his perch.
"What I'm just getting tired (of) a little bit is to get that target on my back all the time," added Alcaraz, who said Medvedev, too, played at a level higher than he'd seen from the Russian before.
"He was playing unreal, I've got to say," Alcaraz said. "I have never seen, to be honest, playing Daniil like this."
But Alcaraz knows it's the price of excellence, and he tries to tune out the expectations.
"I have to accept it," he said. "But after everything I just realized what I had to do and what I have to think before every match and before every tournament, and it is just playing for me, playing for my team, and for my close people.
"I'm not thinking about I need to win or I have to win.
"It's just about chasing my goals, chasing what I just set up before every tournament. That's my mindset, so I'm not getting tired about the people thinking I have to win every match."
