Leading 4-1 after the first leg at the Nou Camp, Barca were beaten 3-0 in Italy to exit at the quarter-final stage on away goals.
The players reportedly pinned the blame for this humiliation squarely on Valverde, telling him he should have set them up to deal with Roma’s physical strengths.
One player, according to Spanish newspaper Sport, told the manager: ‘Boss, this was a game for physical players.’
The players are said to doubt Valverde’s tactical nous, even while admiring his man-management abilities.
It is reported that Valverde listened to his players’ complaints, but did not give an answer immediately.
The defeat to Roma has put a negative slant on Barca’s season, despite their all-conquering form domestically.
They are yet to lose in La Liga this season – and have gone 40 league matches unbeaten – and could become the first invincible side in Spanish league history.
They are also on for a domestic double, as they face Sevilla in the Copa del Rey final on May 6.