Wigan came flying out of the blocks and led 2-0 after 25 minutes through Roger Espinoza and Jordi Gomez.
But the Dons shocked the DW Stadium by going in level at the break thanks to two strikes from Ben Reeves.
Patrick Bamford levelled with eight minutes left, and it was the visitors who were pushing for the winner in the closing stages.
But rather than be happy with holding the holders, Robinson felt his men deserved more.
"I'm disappointed we've not won the game to be honest," he said.
"I'm used to performance levels like that to be fair, because I have such a good group of players.
"They are so determined and never know when to die.
"Eight of the 14 who took to the field were aged 22 and under - you try and find another team in the country who can say they same. There aren't any.
"That shows you how far we've come and what we're trying to do here.
"That's what I'm most proud of here.
"I've got a core of good senior players who have really driven the younger players on."
The Dons did well to stay in the game during a first half when Wigan threw everything at them and threatened to go out of sight.
"We struggled to come to terms with the intensity of the way they pressed us from the off," Robinson recognised.
"To come out of the blocks the way they did was remarkable.
"We have only played two non-league teams to get to this stage, and we have never been put under this kind of pressure.
"We've also played a lot of football recently, which has taken an awful lot out of us.
"We've got one of the smallest and youngest squads in the league, and that ensured we found it difficult to get to grips with the game early on."
Robinson also hailed loan star Bamford, who marked his last game for the club before joining Derby from Chelsea with the goal that sets up a replay later this month.
"The whole football club has seen how much we've developed that lad while he's been here," added Robinson.
"Four months ago, there weren't many takers for his services. Now, 17 goals later, and suddenly everyone is talking about him.
"He's worked very hard, and to score that many goals at 20 years of age is fantastic.
"Derby have got themselves a very talented young player, but on the flip side we have lost a very talented young player.
"He is going to be a very top player, and I'm just pleased we've had the opportunity of working with him."
- Sports & Recreation
- Roger Espinoza
- Ali Al Habsi
- Patrick Bamford
- Callum McManaman