Tottenham had already confirmed top spot in Group H before Wednesday night's routine 3-0 Wembley win over Apoel Nicosia, with Spurs winning three of four games against Real Madrid and Borussia Dortmund to finish the group stages with 16 points.
The last two English clubs to finish the Champions League group stage with 16 points from 18 reached the final - Arsenal in 2006 and Manchester United a year later - and Pochettino encouraged Tottenham fans to "dream" of a repeat after last night’s win at Wembley.
Rose admitted that while German giants Bayern Munich would be a tough test for Spurs, the north London club are ready for whoever Monday's last-16 draw pits them against.
"I wouldn’t like Bayern," said Rose. "But we don’t fear anybody. "The manager would prefer us to have one of the top teams. He relishes those sorts of games.
"We’ve proved this season that we do turn up in these games and whoever is out there, we are confident we can beat anybody. We’ve proved that throughout the group stage."
Basel, Sevilla, Shakhtar Donetsk and Porto are their other possible opponents, and none will relish a trip to Wembley after Spurs finished the group stage with more points than anyone else this season and the most for an English side in a decade.
"It’s not easy to go to the Bernabeu and get a point," Rose said. "And it’s not easy to beat Real Madrid convincingly here [at Wembley]. I hope teams look at those performances and realise we are a team to be feared."
Last night, Apoel showed little appetite to claim a result which could have secured them a place in the Europa League, although their fans in a crowd of 42,679 never stopped believing as they bounced up and down throughout the match.
Fernando Llorente scored his first Tottenham goal on his 17th appearance, trapping Serge Aurier’s cross, swivelling and finishing calmly after 20 minutes. The striker’s deft touch also made Spurs’ second soon after, as he played a quick one-two with Heung-min Son, who curled home his fourth goal in five starts.
Llorente, a 32-year-old World Cup winner, was not supposed to suffer the teething problems which typically plague deadline-day signings and his subdued form, culminating in a bad miss against Leicester last week, has made Pochettino’s decision to opt for experience over youth look misguided.
"The striker needs to feel the net. They wait week after week and if they don’t score they are always very nervous," Pochettino said of Llorente. "It’s not only about playing, It’s about scoring. He’s so happy now. With more confidence and belief, he is going to help the team more."
Llorente’s improvement and an assured display from 19-year-old centre-half Juan Foyth will be particularly welcome for Spurs, who have six games before Boxing Day and three fixtures in five days at the start of January.
Pochettino, whose side had won just won of five games going into last night’s match, might be dreaming of the Champions League Final in Kiev but he admitted his team had "expended a lot of energy" in Europe, which may have damaged their League form.
Spurs, along with the other four English clubs, have a 10-week wait until the knockout stage, in March, and in the meantime they must ensure they remain in contention to qualify for next year’s competition, starting against Stoke at Wembley on Saturday.
Pochettino, though, could not resist looking a little further ahead. "Now we need to show that we can cope with the pressure of the Champions League and compete to arrive in the semi-final or final," he said.