The result was a blow for Socceroos defender Jordan Bos who had joined his boyhood club during the off-season and hoped to play with them in Europe's top club competition.
The former Melbourne City left-back had set up the winning goal when Fenerbahce lost 2-1 in the Netherlands last week.
The Istanbul club fell further behind in the second leg of Tuesday's third qualifying round clash when Feyenoord defender Tsuyoshi Watanabe scored a 41st-minute opener.
Mourinho's team rallied quickly with two goals before halftime — the second by Colombia forward Jhon Duran, on a season-long loan from Saudi club Al Nassr — on the way to a 5-2 win.
That meant Fenerbahce advanced 6-4 on aggregate. They will host Benfica in the first leg of the play-off round next week with a place in the lucrative 36-team league phase, where the Turkish giants haven't featured in 17 years, at stake.
"Compared to last season, the decisive factor today was our fans," said Mourinho.
"When the scoreline dropped to 3-1, there was a positive feeling on the pitch. That was the difference compared to last season.
"I think we deserved more than the defeat in Rotterdam ... Overall, I think the better side advanced."
Benfica were held to a nil-all draw in Lisbon by Nice but progressed after winning 2-0 in the south of France six days ago.
Daniel Arzani, another of Tony Popovic's European-based Australian players, didn't feature in Ferencvaros' 3-0 defeat of Bulgaria's Ludogorets. That took the Hungarian side through 3-0 on aggregate.
Elsewhere, Glasgow Rangers advanced 4-2 on aggregate despite a 2-1 loss in the Czech Republic to Viktoria Plzen.
The Scottish club will host the first leg of their play-off next week against Belgians Club Brugge, who got three second-half goals in a 3-2 comeback win over Salzburg in Austria to move on 4-2 on aggregate.
Russian-owned Pafos, the champions of Cyprus, beat Dynamo Kyiv of Ukraine 2-0 to advance 3-0 on aggregate.
FC Copenhagen beat near neighbours Malmo 5-0, one week after a scoreless draw on the other side of the Oresund Bridge that connects Denmark and Sweden. Copenhagen's reward is a two-legged play-off against Swiss champions Basel.
1991 European Cup champions Crvena zvezda of Serbia also progressed, along with Qarabag of Azerbaijan and Kazakhstan's Kairat Almaty.
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