Hughes, who was sacked by Stoke City in January and has only been given a contract until the end of the season after replacing Mauricio Pellegrino, said he is looking forward to the challenge of keeping Southampton up.
The hosts started brightly and controlled possession early on, and it was Gavin Massey with a volleyed first effort from a Sam Morsy knockdown that he fired just over the Saints goal.
Still, Hughes could count himself slightly fortunate not to suffer the same fate that befell Bournemouth, West Ham and Manchester City - all victims of Wigan's FA Cup run.
Pierre-Emile Hojbjerg hooked in a 62nd-minute corner for his first Saints goal and Manolo Gabbiadini then had a 73rd-minute penalty brilliantly saved by Christian Walton before Cedric Soares added a second in stoppage time.
Cook can call upon the prolific Will Grigg though and the striker has already notched seven goals in this season's FA Cup, including the victor against Manchester City in the last round.
"I have been really impressed with the quality of the talent I have".
FA Cup match report Swansea City v Tottenham Hotspur 17 March 2018
That was all the more impressive in the absence of their talisman Harry Kane , who is ruled out until April with an ankle injury. Tottenham have had to come to terms with the disappointment of being knocked out of the Champions League by Juventus last week.
They have lost just twice in their last 23 matches in all competitions (W14, D7).
'Wigan were an absolute credit to their manager and their fans, I congratulate them and they pushed us hard, ' he continued.
'People have questioned this group, and my appointment.it's only a start but it's a statement of intent.
Wigan manage to create a number of first-half chances as they produced another terrific performance against a Premier League side. The first half, we were excellent.
But from another Tadic corner from the left, the Dane turned it goalwards and Dan Burn was unable to keep it out.
Since they were relegated from the Premier League in 2012-13, Wigan have won six FA Cup ties against top-flight opposition, double the total of any other non-Premier League side in that time.
Portuguese right back Cedric finally sealed the win on a counter-attack in injury time.