The Baggies looked to have secured all three points when Thievy Bifouma found the net in the 93rd minute, but they were to be denied as Mats Moller Daehli struck with just seconds left to earn the Bluebirds a point.
Solskjaer told BBC Sport: "Finally my boys got the luck they deserved. To get a point was very important because to have picked them up after a defeat would have been difficult.
"If we had lost this game, then West Brom are away from us and we would not have been able to claw them back.
"My players knew how important that point is. Now they can get more in the coming weeks."
Cardiff are 18th in the Premier League following the draw.