When the match is played with two legs, then of course there will still be a chance for the team that lost the first leg. After all, the team that lost in the first leg also at least has the quality to make a comeback in the second leg later. About Arsenal, despite losing 2-0 in the first leg but yes, I am personally still quite confident Arsenal are also able to make a comeback in the second leg later although indeed, of course it will be very difficult to beat Newcastle with an aggregate of two goals like that.
It's more possible if Arsenal only lost with 1 goal difference in the first leg, but in fact they lost it with two goal difference. The opponent is Newcastle United, a strong one, so two goal difference is very big barrier like a mountain with Arsenal. They will have small chance to beat Newcatle United with more than two goals, but maybe they will try and hope that beating Newcastle United with only two goals, then wait for extra halfs or penalties.
But about Liverpool, because they only lost with a thin score of 1-0, then of course Liverpool still have a very big chance to beat Tottenham in the second leg later.
Liverpool has only 1 goal difference defeat and with their good attacking power, they can beat Tottenham Hotspur in a second leg with 2+ goal difference and become a winner in this pair after two legs. They have better chance than Arsenal to go next after the second leg matches.
We can only run analysis but the actual job is done on the pitch by 22 players, if Arsenal prepare themselves well with the needed hunger and motivation of getting to the finals than Newcastle, i see no reason why they won't score 3 or more goals without conceding to advance to the finals and at the same time, Tottenham can also defeat Liverpool at Anfield to advance to the finals, I'm not saying it gonna happen like this but this is football and anything is possible.