Goals from Samuel Eto'o and Mario Balotelli meant Inter finished second in Group F and so will face one of the group winners in February and March's first knockout round, although they cannot meet fellow Italians Fiorentina.
"We know the English have an intensity in their play completely different to ours. We know all about the Spanish sides from La Liga," Mourinho, whose side lost to Manchester United in last season's last 16, told a news conference.
"Bordeaux have won a group with Juventus and Bayern Munich and play with pace, intensity and young players. It will be a difficult draw."
Some media reports and pundits had said the Portuguese could have been sacked if Inter, long starved of success in Europe, had lost to the Russians and gone out of the Champions League.
"Journalists don't decide, ex-players don't decide. If someone at the club with the authority decides, that's fine with me," he said after playing three upfront in a bold bid to win.
"We have played with an attacking lineup, it would have been difficult to play with a more offensive side. It seems a normal and correct result."
Rubin coach Kurban Berdyev, whose team now drop into the Europa League, bemoaned the absence of the injured Roman Sharonov and Alexander Bukharov among others.
"All of them are good players. To be without them made our task harder. Some of our players tonight lacked experience," he said.
"At start of the second half we started to be more decisive, I can't say I am dissatisfied with the performance, just the result."
