England Under-21 forward Saido Berahino was left on the West Brom bench and James Morrison started in midfield as Mel's side put on a united front following reports of dressing room unrest in the wake of last weekend's 3-3 draw at Cardiff.
There was, though, no late drama in Norfolk, where a fine goal from Morgan Amalfitano on 16 minutes proved enough to settle what was for most a scrappy affair, although Norwich did twice hit the woodwork in the second half.
"A team that has displayed discipline on the pitch and has played as they did today, well and together, demonstrates that there is a good spirit in the camp and that we are a family," said Spaniard Mel.
"I think the players have shown today exactly what they want and how to go about achieving it. Both Saido and James, plus all the players, have just shown how important they are for us."
West Brom moved above Norwich into 16th place and are five points clear of the relegation zone, having played a match less than the teams around them.
Mel said: "These three points really move us closer to the end and make our route a lot easier.
"I think the Tottenham game next week is really important. If we are able to win against Tottenham the future for us will be a very happy one."
The second successive defeat for the Canaries - whose players had offered to refund the away supporters at Swansea last weekend - was met by loud boos at the final whistle, as hundreds of clapper boards, which had been put on the seats to help improve the atmosphere at Carrow Road, were thrown onto the pitch one appearing to strike Norwich manager Chris Hughton.
The home side could have taken an early lead through Johan Elmander just before West Brom's goal and saw efforts from Gary Hooper and Robert Snodgrass hit the woodwork.
Hughton called for a sense of perspective after what was a first defeat at Carrow Road in 2014.
"The frustration is we conceded an early goal in the game which gave them a lift, and they then set back and we did not show enough quality and guile to exploit what was fairly rigid West Brom side," he said.
"We hit the woodwork twice, but we need to show more than that and did not work our goalkeeper enough.
"I am not so sure we deserved to lose it, but we certainly did not show enough to win it."
Norwich head to Fulham next weekend, and are still looking anxiously over their shoulders ahead of their final games against Liverpool, Chelsea, Manchester United and Arsenal.
There were loud calls for Hughton to be sacked towards the end of the match.
Hughton said: "It is disappointing, but it is a reaction to what they are seeing. It is frustration that we are all feeling.
"At this moment, we need everybody pulling in the right direction.
"So I can understand the frustration and it is something we have to accept and get on with.
"At some stage we have to close this game down, and realise we have a tough away game at Fulham next week, then four more before the end of the season.
"We have to do as well as we can in these five games to get the points we need.
"At the moment, the Fulham game has become the biggest of the season.
"I understand frustrations and it is normal, but we have to understand it is us as a group and everybody is going to get us the results we need."