After falling behind to the Baggies - who had struck the post twice in the first half - United replied with two quick goals, courtesy of an own goal from George Harmon and a debut strike from centre-back Oisin McEntee.
Rosaire Longelo extended Newcastle's lead in the second half and, despite Albion cutting the deficit through Jamie Soule's close-range finish, Yannick Touré sealed three points with a late strike, sending the Magpies into the play-off spots of Premier League 2 division two.
Although Dawson's side continued their promising form, recording a fifth win in their last six league matches, the coach was partially critical of his side and admitted the game was not as one-sided as the score suggested.
"In terms of the result, it's very good and looks like we've played very well but it couldn't be further from the truth," Dawson told nufc.co.uk. "It was a drastically different team to the one that has played the majority of the season.
"We've lost a bit of seniority in the team and it was the first time that the back four had played together. Within the first ten minutes, they (West Brom) hit the post twice and had two great goalscoring opportunities.
"However, our group have got that togetherness and resilience to stick at it and keep trying to work things out and get themselves back into the game.
"We try to stick to the same way of playing, regardless of who our opponents are. The times in which we got the ball down to play, building up the pitch slowly and maintaining good possession, was when we created our best opportunities which led to the goals.
"The game was a good opportunity for others but it will take a bit of work and patience with the group of players we currently have. The result is good but I think as a team, it will take a bit of time to gel."
With Cal Roberts and Nathan Harker missing from the league clash, Dawson confirmed that the duo would be included in the squad for the first-team's Emirates FA Cup third round replay at Blackburn on Tuesday.
And, although the play-offs remain a strong possibility, Dawson is more focused on guiding more of United's youngsters through the ranks to feature at senior level, with Sean Longstaff making his first Premier League start against Chelsea on Saturday.
Dawson added: "The biggest thing that we're looking at is the success of the youngsters so far in that we'll have Sean, Cal and Nathan all involved in the squad (on Tuesday).
"Liam Gibson is now out on loan (at Accrington Stanley) and they are the bits that we are looking at more closely at the moment. Although the play-offs are nice to have as they add extra games and playing against better opposition in the top division, our job is mainly based on how many players can we get into the first-team.
"If then those individual performances can breed teams success then that's great, but it's more about the individual and getting the next player through on a more regular basis."
