Neil Redfearn's side, competing in their second Northern Group D fixture, required a positive result to maintain their hopes of progressing to the knockout stages but trailed by two goals at half time following strikes from forward Fejiri Okenabirhie and Jason Cummings.
And, despite United's dominant second half display, which saw Allan hit the crossbar and Victor Fernández strike the post, Dave Edwards' late finish wrapped up Shrewsbury's victory and knocked United's second-string out at the group stages.
"I don't think it was a fair result," Allan told nufc.co.uk. "If you look at the first 20 minutes and then the whole of the second half, we were the much better team. We've played a League One side off the park and the scoreline flatters them.
"We've had a lot of chances in front of goal. Three or four balls have flashed across the box where you've got to have somebody on the end of it. The goals we've conceded are sloppy and we need to look at them to try and cut them out.
"There are a lot of positives to take but then again, we know we have to finish our chances. That's football. If you take the chance early on and late on, it makes a game of it but three-nil isn't a good result."
Although United's youngsters are unable to progress into the last 32 of the Leasing.com Trophy, Newcastle are still to face Port Vale for their final Group D clash in November and Allan believes the squad need to bow out of the competition in a positive manner.
The Newcastle-born forward was part of the under-21 side which reached the Northern Section quarter-finals last term in which the young Magpies won all three of their group clashes.
The 19-year-old added: "If you look at the starting eleven, there is only about four of five players that started in this competition last season. It's a totally different bunch of players but we want to go to Port Vale in the next game and play for pride, trying to give ourselves a name. It'll be a great occasion to play on.
"We lost quite a few players out on loan compared to last season but that's just football. The lads need that experience elsewhere so it's a good one but for us we'll take it on the chin and try to rectify it."
