Espanyol's academy graduate Oscar Melendo crashed in the only goal of the game in the 88th minute after Messi had his spot-kick turned away by former Real Madrid goalkeeper Diego Lopez earlier in the second half.
And Valverde feels that, although it is only a slender deficit, Espanyol are favourites ahead of next Thursday's return leg in Camp Nou.
"We knew [a defeat] was going to arrive at some point", Busquets said. From there, the game went in a direction we didn't want and we complicated things.
Barcelona hit their stride in the coach's new 4-4-2 system but Suarez lagged behind, missing Neymar, who left for Paris St Germain in the middle of previous year. "We tried to keep the run going as long as possible, but it wasn't to be tonight". Espanyol sensed that and sat deep in the first half, making the visitors work hard for their chances.
"I quite liked how my team played", the Barca coach said in his postgame news conference.
The 30-year-old failed to score in any of Barcelona's six Champions League group games, missed easy chances and was bereft of confidence, despite Valverde consistently starting him.
Inter are restricted by how much transfer business they can do in January due to Financial Fair Play rules, and are unable to purchase Rafinha outright until the summer.