With the game divided into four 20-minute periods to give Easterby and opposite number Rob Baxter the chance to see the majority of their squads in action, the Scarlets trailed 13-3 at the end of the first quarter but hit back to lead 15-13 at the half-time break.
The hosts failed to add to that tally in the final 40 minutes, however, and a Henry Slade penalty and a late converted try from Chiefs second row Will Carrick-Smith saw Exeter head back to Devon with a repeat of last season's Heineken Cup double over the Scarlets.
"I'm not too disheartened. We've still got a lot of players to come back," said Easterby.
"The last try flattered them a bit. I think 16-15 would have been a better reflection of the game.
"It's difficult to assess the game as both teams had to deal with playing in pretty poor conditions and the ball was pretty greasy. We made some errors and put some pressure on ourselves, but we also played some nice stuff at times.
"What's important is that we got a lot of players game time in the first outing of the season. I'm confident things will build nicely throughout pre-season."
Scrum-half Gareth Davies and wing Jordan Williams scored first-half tries for the Scarlets, with Steve Shingler marking his return from London Irish with a conversion and a penalty.
Former Scarlets lock Damien Welch crossed for Exeter's opening try, while fly-halves Gareth Steenson and Slade kicked a total of 13 points between them.
The Scarlets now turn their attentions to Sunday's trip to Oxford to face recently relegated London Welsh, before finishing their pre-season preparations with another away tie at Nigel Davies' Gloucester.
Easterby and co then open their league season with a home clash against reigning RaboDirect PRO12 Champions Leinster at Parc y Scarlets on Friday, September 6.