Rangers' next assignment is this weekend's SPL game with United at Tannadice and Fleck believes he and fellow youngsters Danny Wilson and Jordan McMillan proved the club have the squad to cope with their current injury crisis.
"Dundee were very good and made it difficult for us," Fleck told Rangers' official website.
"But that makes the result even more pleasing.
"To come up here and get a win with so many players out says a lot about the character this squad has.
"Hopefully, we can now build on this performance when we come back up here to Tannadice this weekend."
Tuesday saw Fleck net for the first time since January and he added: "It was a great night for me and I really enjoyed the game although it was tough.
"I thought Nacho (Novo) did great for my goal as he played a great pass to me.
"He could have gone himself but played me in and I was absolutely delighted to score at the end.
"I enjoy playing up front in the second half as that is my natural position but I thought Danny and Jordan did really well considering it was their debuts.
"Danny is getting bigger and stronger every couple of weeks, which is helping him a lot.
"He has a great future, which can only be good for the club."