The manager, who was ecstatic with the character shown by his side, hopes the performance can help change his side's fortunes but Pepe Mel was left ruing dropped points
The 41-year-old saw his side start terribly with two early goals from Morgan Amalfitano and Graham Dorrans earning the Baggies an early lead before Jordon Mutch pulled one back.
But an impressive second-half performance from the Bluebirds saw them dominate proceedings and pull level in the final minute of the game, which Solskjaer believes can inspire them for the rest of the season.
"I’m so happy for the players and the fans that we got the goal we deserved as we never deserved to lose that game – no chance. The reaction was magnificent," he admitted in his press conference.
"Scoring goals is the name of the game and we’ve got loads of goals in us. But we need to stop conceding that many but then again today we didn’t have many chances against us.
"In the second half we were in complete control. When they scored you think ‘that’s it’ but the lads have got some character. I think our dressing room is a bit happier than theirs at the moment.
"I think it can be [a turning point] because we’ve been waiting 32 games to get that luck and finally we’ve got it."
But a disappointed Pepe Mel was left dumbfounded by his side's inability to keep hold of both their early two-goal lead and what he feels should have been a late winner from Thievy.
"[We're] quite bad really and the spirits in the changing room at the minute are quite bad," he admitted. "The fans will see that we played a good game and the result should have been a better one really.
"A wrong decision was made today. We were 3-2 up with just 30 seconds remaining on the counter attack and that really should have been the end of the game.
"Of course, the fact they came into it at 2-1 gave them a lot of confidence and Cardiff also needed a win so they needed to attack attacked.
"I’m sad we didn’t win the points for them as the atmosphere was incredible. With both looking for the same things and both teams looking for the win I think frankly today West Brom were better."