The Spanish head coach looked set to begin his Hawthorns reign with a defeat when Kevin Mirallas put Everton ahead shortly before the interval.
But a 75th-minute leveller from defender Diego Lugano secured a point for West Brom, and Mel - who took over earlier this month following the dismissal of Steve Clarke - expressed satisfaction with the performance of his players against a team striving for Champions League football.
"For me the performance was very good," he told Sky Sports.
"In the first half we were too open but in the second half we were compact. Everton is a team that is very, very strong. Tonight was a difficult match for me and my team."
Despite the pleasing start, Mel insists that there is still more work to be done, and hopes to sign a striker in the January transfer window.
"It is only the first week, I need to work," he added. "The players are hungry, for me that it is important.
"Shane Long is out, I think the team is very well, I need one more striker, but with [Nicolas] Anelka, [Victor] Anichebe, [Matej] Vydra I am happy."