A solitary 44th minute strike from Youssef Sofiane earned all three points against a strong Rams side who have won the Reserve League title twice in the last three seasons.
After veteran keeper Raimond Van der Gouw, Irish defender Clive Delaney was the oldest player in the Hammers team, at just 23-years-old, and not a single member of the starting line-up had any first team experience.
Said Roger: "It was a terrific team performance, they showed big hearts and I am extremely proud of the young lads who came in and did so well.
"We played some good stuff when we could, and we dug in with determination when we had to. Derby have an excellent record at reserve level, their team is very settled, and they are pushing for the title again this season.
"The lads responded to that and thoroughly deserved the victory. We scored a terrific goal and I thought the back four were superb. Elliott Ward and Clive Delaney won everything in the air, the two full-backs did their job and David Noble and Daryl McMahon in the centre of midfield protected them well."
While it was clearly a fantastic team performance that saw Derby off, the Hammers coach was particularly impressed by the display of young Irish midfielder McMahon, who has improved greatly in recent months and is starting to realise his potential.
"I thought Daryl had his best game for West Ham tonight," said Roger. "There is no doubting his ability, but we have asked him if he can do it for 90 minutes and show that he can compete and work hard when he has to, and tonight he proved that he can.
"He is heading in the right direction now, and he needs to perform like that regularly. All the young lads know that they can't rest on one performance, they have to push on and find that desired level of consistency."
Despite the fact that Hammers have lost just once in 12 home games this season - against Southampton last week - the victory against Derby marked only the third home win of the season. The other eight have all been draws - many of which should have produced three points rather than one.
Says Roger: "We have drawn so many matches and the main reason is because we haven't had a regular goalscorer in the team all season. Richard Garcia is our top scorer with four goals and there have been many tight games that we would have won with an out-and-out goalscorer up front.
"I think we have the best defensive record in the division, but the worst scoring record, which is a crazy situation, but it is just something we have to get on with. We have been fielding a very young side for most of the season and they are all learning from the experience of playing regular senior football."