A section of Southampton supporters voiced their displeasure at Pellegrino during and after the match at St Mary's, but Romeu stressed that it is the players who must shoulder the responsibility for the club's poor form.
"It's not the manager's problem. We are the ones playing, and the ones that have to change this," he is quoted as saying by The Telegraph.
"This season we have conceded too many easy goals. Then closing the game down, we have had too many times when we have lost points in the last minutes, so we need to know how to close the games, how to play under pressure, and then we will know how to get points.
"It is going to be very, very tight until the end [of the season]. Every point is going to be important."
Southampton have won just one of their last 14 Premier League games.