Dave Jones said: "We never played as well as we are capable of and they had a few chances.
"Sometimes you have a bad day at the office but perseverance has brought us the victory.
"It was a definite penalty and a definite sending off as the lad could have broken Darcy Blake's leg.
"If the penalty had gone in it would have been a different story in the second half.
"It wasn't a bad spot-kick from Peter Whittingham but he does need a goal as things haven't gone so well for him this season."
Jones added: "Andy Keogh never had the best of games but he kept going and scored a typical striker's goal so he will be delighted to get off the mark.
"We were poor at decision making today but eventually found the quality to take all three points.
"We have missed our injured players but I must be careful not to rush them back too soon."
Regardless of the performance, the result saw Cardiff bounce back after successive defeats and got their promotion charge back on track.
Millwall, meanwhile, continue their slump in form after a positive start to the season.
The defeat, coming after last weekend's 6-1 home reverse to Watford, extends their winless run to five games.
But manager Kenny Jackett justifiably remained upbeat after the manner of this performance.
"We are very disappointed with the result but we have plenty of positives to take out of the game because we did a lot of things right," he said.
"On level terms we had a good game on and took a deserved lead but, after going down to 10 men, we had to sit back and frustrate them, but even then we had chances.
"Liam Trotter was harshly treated to be sent off but I can't say any more because I will get into trouble.
"David Forde made a good save from a penalty and I was hopeful we could get something out of the game until the last minute when they scored.
"The lads put in a lot of hard work and the dressing room is down at the moment but any mistakes we made today were honest ones and there was a lot for us to build on."