The 20-year-old forward, who made his senior debut in United's Emirates FA Cup third round win against Rochdale at St, James' Park last month, netted the match winner - his 13th goal of the season - from close range in the Group C clash.
Allan then saw a penalty saved in the second half by Baggies goalkeeper Josh Griffiths but United's second-string deservedly earned three points to keep their hopes of reaching the last 16 firmly on track.
"Everyone is pleased with the result," Allan told nufc.co.uk. "We've got two clean sheets in a row now (following a 4-0 win at Swansea last week) and I think we've tightened up at the back and are doing really well. We need to keep that going and take it into the next game against Sunderland.
"At the start of the season, I think it was an area that we needed to close up on. We conceded quite a few goals but now that's improving and it gives the forwards more chances to do their thing and once they do their bit, there's a great chance of winning games.
"All the lads said after the match that although it was a one-nil game, we had a lot of chances, especially on the break. I think that's a positive and if we can fix that, then we can beat anyone.
"We're not left in all the cup competitions so this is a big one for us. We managed to do well in it last year (reaching the final) so we just want to go as far as we can and this win is a big step closer to doing that."
Allan, an unused substitute in three of Newcastle's four previous fixtures, admitted he has been pleased with his goalscoring form for the under-23s this term after netting only five times over the duration of the 2018/19 campaign.
The Newcastle-born forward added that he is also relishing a return to St. James' Park as Newcastle host local rivals Sunderland in Premier League 2, bidding to win three successive games for the first time since April.
"I was pleased to get another goal," Allan said. "I feel like I'm doing well this season and probably could have got another today after missing the penalty. To be honest, I'm just happy that we were able to get the win and it gives us a really good chance of going through.
"It couldn't have went much better with the two games before the game against Sunderland so everyone is buzzing. It should be a big one at St. James' and hopefully we can get the job done there.
"The last time at St. James' was special for me so hopefully I can get a similar sort of feeling like that again on Friday night."
Photograph courtesy of West Bromwich Albion
