The Reds' league form suffered as a result of their run to the final of UEFA's showpiece competition in the latter stages of the previous campaign, eventually holding on for a fourth-place finish in the English top flight.
Salah is upbeat about Liverpool's ability to juggle European and domestic commitments over the next eight months, however, with neither competition taking priority over the other.
"Last season we knocked out Manchester City, then Roma, who had just beaten Barca in the quarter-finals. Each time, they were incredible games," he told France Football ahead of his side's Group C opener against Paris Saint-Germain.
"We played against teams challenging for the title and we still managed to reach the final, so of course we can do it again. I'm sure of it. We can even win both, the Champions League and the Premier League. I don't want us to put pressure on ourselves, but yes, everything is possible.
"It's a good draw with some good teams. PSG have some very good individuals and a great team. I'm looking forward to playing them. I'm looking forward to a very enjoyable and intense encounter."
Liverpool have won all five of their Premier League games so far this season to join Chelsea on 15 points from 15.