Mel's side were outplayed by Fulham in the first half and deservedly fell behind just before the half-hour mark through a strike from midfielder Ashkan Dejagah.
However, the hosts fought back well and claimed a point in fortuitous circumstances four minutes from time as Fulham goalkeeper Maarten Stekelenburg allowed a weak effort from substitute Matej Vydra to roll under his body and over the line.
The draw marked the fourth time that West Brom have come from a goal down to take a point under Mel's stewardship.
But that is nothing more than cold comfort for Mel, who is still awaiting his first win since taking over at The Hawthorns last month.
"Before the match in my head all that is possible is three points," Mel said.
"We should have more points, the first half my team is too open, it's a problem.
"It's an important point, but I think West Brom had a lot of chances to win the match. Sorry but for me the best player is the goalkeeper of Fulham."
West Brom are just a point above the drop zone in 16th but, while Mel is desperate to end his wait for a win, the former Real Betis boss is refusing to panic.
"The players are working very hard to win these points but, for everyone's mentality, we need to win a match," he added.
"It's still February. There are still three months left. It's important we stay calm, continue to work hard and look forward with optimism."
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