New England Patriots quarterback Drake Maye, right, and Houston Texans quarterback C.J. Stroud meet on the field following the Patriots’ 41-21 loss on Sunday in Foxborough, Mass. Charles Krupa/Associated Press

FOXBOROUGH, Mass. — Drake Maye got words of encouragement from another high draft pick on Sunday after the New England Patriots lost to the Texans in the rookie’s first career start.

A year ago, Houston’s C.J. Stroud was in Maye’s shoes – a first-year quarterback entrusted to lead the franchise after getting selected early in the draft. Stroud was the No. 2 overall pick, and Maye was taken third.

Stroud lost his first two starts before leading the Texans to the playoffs. Given the sorry state of Maye’s team, the Patriots (1-5) are unlikely to make a similar run.

Still, Maye’s performance in the Patriots’ 41-21 loss to the Texans provided a jolt of energy. He finished 22 of 30 for 243 yards with an 88.3 passer rating. With three touchdown passes, the 22-year-old exceeded the five-game total of Jacoby Brissett, whose ineffectiveness prompted Patriots Coach Jerod Mayo to switch to the rookie.

“I was a little amped at the start for sure. The guys around me were great trying to settle me down, and Jacoby was a big part of that,” Maye said.

Maye took his first snap as an NFL starting QB at 9:08 of the first quarter. His image appearing on the Gillette Stadium video board prompted a huge ovation from the crowd.

“It gave me goosebumps going out there for the first time,” Maye said. “I’m in a great spot with the Patriots here and playing quarterback in the NFL.”

His debut was a mix of positives and learning moments. He overthrew DeMario Douglas for a first-quarter interception but connected with Douglas for a 35-yard touchdown in the fourth quarter.

“I love how he gained confidence throughout the game and I thought it was a good first game for him,” Douglas said.

Patriots fans are hoping Maye can emerge as the franchise’s long-sought-after solution in the post-Tom Brady era, and they found reason to be encouraged late in the first half. Looking downfield, Maye unleashed a perfect throw that dropped into Kayshon Boutte’s arms for a 40-yard touchdown that got New England within 14-7.

“His competitiveness was great,” said tight end Hunter Henry, who caught a TD pass from Maye in the third quarter.

Maye also rushed for a team-best 38 yards, as his ability to scramble and keep plays alive added an element to a New England offense that regressed after winning its season opener at Cincinnati and taking Seattle to overtime in Week 2. He also learned the importance of taking care of the ball – one of Houston’s four sacks led to a fumble that gave the Texans the ball at the Patriots 10-yard line.

“I think I took a couple sacks where I could have thrown it away or thrown check-downs instead of getting a sack,” Maye said. “Just kept hurting ourselves, and in this league, these teams are too good to do that. But some great stuff to watch on film.”

Stroud was asked about the words of encouragement he gave Maye when the two young QBs crossed paths after the final whistle.

“Just be yourself, you know. Everything that got you here will take care of where you want to go and really just trust yourself. Trust that you’ll eventually figure it out. You’ll have bad days. You’ll have good days. There are days where you’ll look at yourself like, man, I’m the worst quarterback in the world, but it’s always about getting up the next day and keep going,” Stroud said. “I thought he played really solid. Definitely feel like he’ll get better and better as he keeps going.”