Messi and Busquets started Saturday's 1-1 draw in LaLiga on the bench, with Valverde having an eye on a trip to Tottenham in the Champions League.
Real Madrid were thrashed by Sevilla as they and Barcelona lost a La Liga game on the same day for the first time since 4 January 2015.
"I believed that Leo and Busquets had to rest because we have a very complicated match on Wednesday", Valverde said.
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Messi also stated, "You are threatening me, you are threatening me".
"We had many chances but couldn't take advantage of them", Barcelona forward Luis Suarez said.
Leganes goalkeeper Ivan Cuellar pulled off a stunning double save to thwart Coutinho and Ivan Rakitic from close range in the closing minutes while Sergi Roberto skied a good opportunity as the unfancied hosts held on to record their first top-flight win over Barcelona.
Most worrying is the fact they have conceded eight goals already but, while admitting there are areas to improve, Messi said there is no need to panic at this stage of the campaign. FC Barcelona signed players like Arturo Vidal to bolster their midfield department but still believe they have not yet completely filled the absence of Iniesta. Messi came close to scoring the victor with a late free kick, and after the match was shown a yellow card for complaining to the referee.
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De Marcos stunned the Camp Nou following a set piece just before half time to give Bilbao the lead and Valverde didn't waste too long in trying to rectify the situation after the break.
"We can not depend on Messi solving everything", Suarez said. It was winless since the first round.
Second place is occupied by former Real Madrid star Emilio Butragueño, who clocked up a half century of games without being on the losing side in the league between 1988 and 1989.
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