Son Heung-min's header 11 minutes from time moved Spurs up to sixth and within six points of Chelsea in the battle for a top-four finish.
Tottenham captain Hugo Lloris returned to training earlier this month, but was not expected to feature until early February.
Mourinho said there was no issue between himself and Rose, who has also fallen out of favour with England manager Gareth Southgate.
The 21-year-old signed an 18-month loan deal with an option to make the transfer permanent for a reported £56 million.
The arrival of Fernandes would give Tottenham another option in midfield after Mourinho saw France international Moussa Sissoko ruled out until April after undergoing knee surgery.
Spurs killed off second-tier Middlesbrough within the first 15 minutes of the third round replay at the Tottenham Hotspur Stadium.
Harry Kane needed surgery on his left hamstring after suffering a ruptured tendon against Southampton on New Year's Day.
Kane was injured in the second half of Wednesday's Premier League game against Southampton.
Chelsea boss Frank Lampard is expected to make a big splash after being unable to sign players in the summer window due to the club's transfer ban.
Mourinho was booked by referee Mike Dean in the 77th minute after the Portuguese approached the Southampton bench.
Kane picked up the problem in the process of scoring an offside goal, sparking fears he could be set for a lengthy spell on the sidelines.
Chelsea beat Tottenham in a big win for Frank Lampard over his former mentor Jose Mourinho on Sunday, but the gap between the two is back down to three points.
The ugly scenes overshadowed the Willian double that gave Lampard a memorable triumph at the expense of his former Chelsea manager Mourinho.
Spurs will hope to make further inroads against Wolves on Sunday in a bid to get back to where Mourinho says they belong.
Tottenham currently hold the seventh position on the Premier League table with 23 points.