Mel's side looked to be heading for defeat when Daniel Sturridge put fourth-placed Liverpool ahead after 24 minutes with a close-range finish.
However, the hosts responded well and earned a point as Victor Anichebe capitalised on a poorly placed pass from Kolo Toure to level midway through the second half.
The result keeps West Brom in the relegation mire, just one point above the drop zone, but Mel - who confirmed that Jonas Olsson will miss Saturday's trip to Crystal Palace after limping off in the first half - was quick to praise his side's efforts.
"I'm very happy for the players and fans," Mel said. "In the first half we didn't press [Steven] Gerrard and [Jordan] Henderson enough and they caused us problems.
"We pressed much better in the second half and Anichebe's goal came from [Matej] Vydra and [Zoltan] Gera pressing..
"Victor took his goal very well."
The former Real Betis boss also highlighted the display of goalkeeper Ben Foster after the England international pulled off a fine save to prevent Luis Suarez from doubling Liverpool's lead prior to Anichebe's leveller.
"Foster also did good work," Mel added. "He is a very, very good goalkeeper.
"The last game [a 4-3 defeat to Aston Villa on Wednesday] was not good for us but the players are happier now."