Burns went 0-for-4 in his starting debut, as the A's fell to the Astros, 8-1.
"One of the reasons I put him in the leadoff spot is that's where he's comfortable," said Melvin of Oakland's No. 17-ranked prospect. "It's the same thing we did in the spring -- we put him in the leadoff spot, where he's most comfortable -- so we'll let him go out there and do his thing.
"You don't want to put too much pressure on a guy and say you expect too much from him. I just want him to go out and play, have some fun. That would be good enough for me to start."
The 24-year-old Burns, promoted Monday after the A's learned Craig Gentry had a broken right hand, has spent the majority of his professional career batting leadoff. He did it in all 91 games for Double-A Midland this season, batting .250 with a .333 on-base percentage and 51 stolen bases.
He got his feet wet on the big league stage with a pinch-hit at-bat in Monday's game, in which he lined out to right field, and he had a pinch-running opportunity Tuesday.
"It was key to give him the at-bat the other day to get the first at-bat out of the way," said Melvin. "Now go out there and do your thing. That's what I told him: 'Look, I got you leading off, I'm going to give you the same reins I gave you in Spring Training. It's the same game, same dimensions. Don't put too much pressure on your yourself, you've got a lot of guys behind you. Don't feel like you have to go out there and we're relying on you to be productive. Just go out there and do your thing.'
"It can be a little overwhelming, the first big league game. I could tell you that from experience."