That they scored each of their four goals - twice through Willian and then Pedro and Olivier Giroud - by half-time demonstrated they remain capable of reaching the level that led them to last season's Premier League title, and before a period that could define their campaign.
Conte also suggested Willian had played himself into contention to start against Barca by playing a starring role in Friday's win at Stamford Bridge.
"The hat-trick was nearly there, I tried, but the most important thing was the win", Willian said. But it's right to be so.
Hull made the worst possible start as Kevin Stewart was dispossessed by Giroud in the second minute before Willian used the Frenchman as a decoy as he bent his left-footed shot into David Marshall's bottom right corner.
"Jose Mourinho was in charge and Scunny actually went in front, Paul Hayes scored a wonderful goal, and for half an hour the magic of the FA Cup (was alive) and the Scunthorpe supporters were jumping up and down, and everyone had a smile on their faces". In the second half we tried to manage the game and in England that is very hard. As you know, in England that's very hard, because anything can happen. It's very nice. Two clean sheets. "I'm very happy for Willy Caballero, who has shown he is a great goalkeeper".
"We gifted them the opportunities to score goals in the first half and you saw how good their players are when you're up close and personal". This type of game must give us great enthusiasm. I told the players this wasn't the situation we wanted to be in but we tweaked one or two things and improved.
"I think I have to make the best decisions for the team".
But a very different peril awaits on Sunday when they travel to Rochdale to play on a surface Pochettino has described as "not a pitch in a condition to play football". You could see their flair and how they break up play. "It was important to bounce back after some disappointing results".