The youngsters were knocked out of the competition after goals from Bolton forwards Matthew Argent-Barnes and Eddie Brown secured the Trotters' passage to round four.
Jack Young's splendid free kick gave United hope late on but the Magpies made an early exit from the tournament after failing to grab a late equaliser.
But despite the loss, Watson believed the teenagers gave a good account of themselves at the University of Bolton Stadium and deserved a lot more for their efforts.
"There are games where you get beaten and you hold your hands up because you've seen the lads have given a wholehearted performance," Watson told nufc.co.uk.
"It was a really good start. We won many periods in the game and had two great headers which have went straight at the goalkeeper.
"Their attitude was magnificent and we had enough chances to certainly score two or three goals, but it wasn't to be today.
"We're disappointed to be knocked out after showing great commitment and based on the performance I thought they did very well."
After Wanderers doubled their lead in the second half, Watson praised his players' determination in their attempts to find a way back into the match and wished his side could have been more fortunate on the night.
He added: "We have created chances and we always thought if we did that, we can score goals. Unfortunately, it didn't turn out that way but I cannot fault the kids - they've been great and given their all.
"It was a tremendous reaction. After going behind in the first half, we were still disappointed to be going in at the break one goal behind.
"After a magnificent save from the keeper (Dan Langley), they've been given a free header in the box and we could have possibly reacted better than they did.
"Having said that, to come back and get a goal along with creating chances, it was fantastic and made for a good cup tie.
"I just feel for them as they've had a tough season so far and I wanted them to get back into it and take the game further, but it wasn't to be."