The Dutchman was fortunate to stay on the pitch after two late challenges in the second half of Manchester United's 3-0 victory at the Hawthorns on Saturday.
The Dutch striker 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.
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"Yes I think Van Persie should have been sent off - it was a clear second yellow card," Mel 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 sits outside the Premier League bottom three solely by virtue of goal difference.
The Baggies, 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.
"I hope the players respond well to playing under pressure," Mel said. "I'm still confident I can keep West Brom up - the next four matches are very important for us."