Van Persie appeared fortunate to escape a dismissal early in the second half of United's 3-0 victory, as he followed up a reckless challenge on Morgan Amalfitano - for which he was booked - with another late tackle on Steven Reid shortly after.
Despite vehement protests from the hosts, referee Moss opted to give the Dutchman a stern warning instead of a second booking.
Mel's United counterpart David Moyes, seemingly aware of Van Persie's fortune, substituted the striker soon after, with his replacement Danny Welbeck securing the three points with a late goal.
And Mel - who is still awaiting his first win as West Brom boss after seven games in charge - was left to rue Van Persie's reprieve, which came when his side were only one goal down.
"Yes I think Van Persie should have been sent off - it was a clear second yellow card," the Spaniard said.
"If Van Persie had received a red card the game would have been completely different.
"I haven't spoken to the referee about it - what would have been the point? Once the referee's blown there is no going back on it."
Mel was forced to make three substitutions due to injuries before the 65-minute mark on Saturday, with Claudio Yacob, Chris Brunt and Reid all picking up knocks.
And the former Real Betis boss said such "bad luck" meant his hands were tied when it came to attempting to change the flow of the match.
"We weren't able to do anything else despite the fact the game required it," he added.
"Due to the changes we couldn't do anything else."
Following Cardiff City's victory over Fulham later on Saturday, West Brom sit outside the Premier League bottom three solely by virtue of goal difference.
The Midlanders, who have won just two of their last 22 top-flight games, now face a crucial run of fixtures against relegation rivals Swansea City, Hull City, Cardiff and Norwich City.
And Mel believes those upcoming matches could define their season.
"I hope the players respond well to playing under pressure," he said.
"I'm still confident I can keep West Brom up - the next four matches are very important for us."
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