Leading 2-0 from the first leg thanks to late goals from Roberto Firmino and Salah, the Reds looked comfortable for the opening hour of Wednesday's (AEDT) second leg at Anfield.
However, Lautaro Martinez's first goal in the competition since November 2020 – a superb swerving shot from 20 yards – gave Inter serious hope of at least forcing extra time.
Alexis Sanchez's red card 107 seconds later proved damaging, though, as Inter failed to create any further clear-cut opportunities against its Premier League opponent.
The defeat is Liverpool's first at Anfield in all competitions since March 7 last year, a run spanning some 28 matches, and marks just the third time they have lost this season.
But with his side having ultimately done enough to advance 2-1 winners on aggregate, Salah is hoping to use the rare setback to Liverpool's advantage.
"They are a tough team," Salah said. "Even in the away game they were very good. We struggled in the beginning. We had the ball in the second half more.
"The most important thing is that we qualified. The most important thing is the team qualifying. We lost a game but it is a good game for us to take it and learn from it.
"Maybe we got overconfident. It's always important to win, but tonight we hit the post twice, and missed chances.
"But that can happen and the good thing is, it’s not in the Premier League and we have qualified.
"Everyone wants to win the Champions League and the Premier League, so we will fight for both, and let’s see.”
Salah twice hit the frame of the goal, while Joel Matip also sent a header against the crossbar, on what proved to be a frustrating occasion for Jurgen Klopp's side.
He had previously scored eight goals in seven Champions League games this term, but failed to net from an expected goals (xG) return of 0.70 in the second leg.
The Egypt international could afford to laugh off his profligacy as attention instantly turned to Saturday's Premier League contest with Brighton and Hove Albion.
Salah said: "I hit the post twice. It’s OK – maybe I score three next time!"