The hosts restricted Jose Mourinho's men to limited first-half chances but suffered a body blow when Branislav Ivanovic capitalised on slack marking to score in the third minute of stoppage time before the break.
Mel's team weathered considerable pressure after the restart, but laid siege to the Chelsea goal in a stirring final 20 minutes, with Victor Anichebe finding an equaliser - as he did when Liverpool visited The Hawthorns nine days ago – in the 87th minute.
"I am proud with my players," Mel said. "For me, it is good to have different halves.
"In the first half there was good defence – only two chances for Chelsea. And in the second half there was good transition between attack and defence, good counter attack and good mentality.
"If West Brom scored a goal before (we did), for me we could win the match."
The point edges West Brom above Sunderland and out of the relegation zone on goal difference and Mel was hailed a marked improvement from Saturday's abject 3-1 loss at Crystal Palace.
"The players and I need a win but this draw against Chelsea, for us, is good because Chelsea is a big team," he said.
"I think the last match, for us, was very, very bad. We needed to work on focus for this match and they next match is very important too."
Next up, following a warm-weather training break in Spain, are fellow strugglers Fulham in the first of back-to-back home games.
"I think if we play as we did in the second half we'll have no problem to win the games," said Mel, whose team take on reigning champions Manchester United in the second of those matches.
