Wissam Ben Yedder came off the bench to score a brace and send Sevilla through to the quarter-finals, United exiting 2-1 on aggregate after Romelu Lukaku's consolation.
Salah was anonymous as Liverpool lost 2-1 against United in the Premier League on Saturday, with Mourinho's men tightening their grip on second place in the table.
But the Egypt international, joint-top scorer in the league this season, was speedy to show off about Liverpool's place in the quarter-finals.
"The UCL draw can't come soon enough," Salah wrote on Twitter, following by a smiling emoji.
Liverpool knocked out Porto 5-0 on aggregate to book their spot in the quarter-finals of the Champions League, with Jurgen Klopp's men finding out their next opponents on Friday.
Watch the UCL quarter-final draw LIVE and FREE Friday night from 9:55pm (AEDT) on The World Game website and app.