Travers featured on Saturday as Rovers won 1-0 at Ewood Park.
Afterwards, the signing from Bournemouth told Everton's website: “It’s really good to get 90 minutes under my belt.
“I'd say it’s a disappointing result, but we're still early in pre-season. The lads are just getting their fitness levels up. I'm really excited to get my first game early in pre-season and I'm looking forward to the rest of pre-season now.
“It’s nice to be involved and contribute. I made some good saves. Of course, you'll always be disappointed not getting a win, but it's good to be on that pitch and build those minutes.”
Travers added, “It's been really good first week.
“I’ve enjoyed getting to know all the new teammates, all the new staff, and as I say, they've all welcomed me in so well."