The Magpies slipped to their second straight Premier League loss as Saido Berahino scored a penalty for the hosts three minutes from time for the only goal of the game at the Hawthorns.
And the defeat came at a further cost, as Mathieu Debuchy was shown a straight red card for a dangerous tackle on Claudio Yacob midway through the second half, before Coloccini limped off.
Pardew confirmed that Newcastle could be without their Argentinian defender for up to six weeks.
"It has been a bad afternoon," said the Newcastle boss. "Not only do we lose Debuchy but Colo [Coloccini] also looks to have done something to his knee.
"It is early days but we could be looking at four to six weeks out."
Mapou Yanga-Mbiwa replaced Coloccini following the injury, and the Frenchman will likely be asked to deputise in the former Deportivo La Coruna man's absence when Newcastle face Cardiff City in the FA Cup on Saturday.