The Bluebirds dropped to the foot of the Premier League table after their defeat at the Etihad Stadium, but there were positive signs for their new Norwegian manager.
Craig Noone's clever equaliser brought them back into the contest after falling behind to an early Edin Dzeko goal.
And in the second half, both Noone and Jordon Mutch tested Joe Hart before the hosts pulled away again through Yaya Toure and Sergio Aguero.
"We were in the game until 15 minutes to go," Solskjaer told Sky Sports, "and I was very pleased with the response of the lads after the bad start we had.
"That's got to change. We can't just come here and let them do what they want, because we could have been three down after 10 minutes. That mindset's got to change, definitely.
"Then we scored a terrific goal through Nooney, and we had a few other decent efforts I thought. To be still in the game with a quarter of an hour to go, you might have a chance.
"But Yaya Toure is very hard to stop when he goes on one of those runs."
Along with Toure, 26-year-old winger Noone - who joined from Brighton in 2012 - was among the standout players on the pitch.
"He's brilliant - he can go inside or outside, and he's a terrific little footballer," said Solskjaer. "He had a good game. He's got parts of his game he can develop of course, but he'll be a good player for us."
Next up for Cardiff in the league is another tough test at Solskjaer's former club Manchester United and the Bluebirds boss knows his team must be more resilient at Old Trafford.
"The way we started playing after we went 1-0 down was pleasing," he said. "It could have been a long hard day.
"We can't accept defeat before the game. The response was very good and we created chances, but when you go for it towards the end, that's when they hurt you.
"We managed to get a goal in stoppage time though. To score two goals at a place like this is not too bad."
On the potential for more transfer additions this month, he added: "You're always looking in the market for value for money. But in the performance today, we were only lacking in aggression and to start the game on the front foot."
Cardiff goalscorer Noone was delighted to score his first Premier League goal.
He said: "It was amazing to get my first Premier League goal. I'm delighted and it's been hard working through the leagues but I'm glad it has paid off and I have scored in the Premier League
"I was positive when I got the ball and I went on to get a goal. But I'm disappointed in the result obviously but I can take some positives out of my own game and I'll work hard to stay in the team."