The Reds duo both suffered knocks during the 3-1 defeat by Manchester City at the Etihad on Monday Night Football.
Right-back Johnson, 30, limped off late in the second half, forcing Brendan Rodgers' side to finish the game with 10 men.
And Moreno may well have been taken off shortly before full-time when he fell awkwardly on his right ankle, but the away side had used all their substitutes and were already a man down.
Spain Under-21 international Moreno, 20, made his debut in the defeat following a £12million move from Sevilla, but was at fault for City's opener scored by Stefan Jovetic.
Jovetic bagged the second for Manuel Pellegrini's side midway through the second half before substitute Sergio Aguero made it 3-0 with his first touch of the game.
Full-back Pablo Zabaleta scored an unlucky own goal, as Rickie Lambert's header was pushed onto his leg by Joe Hart, to give the Reds a late consolation.
But the loss was an early indication of the current difference between the champions and one of the favourites to challenge this season.