Pulis' side lost out to Edin Dzeko's 66th-minute goal, but had chances themselves as City goalkeeper Joe Hart was fully extended on three occasions by Jason Puncheon, Mile Jedinak and Joel Ward.
Ward also missed a glorious opportunity to equalise a minute after Dzeko's strike when he was left unmarked at a corner and headed wide from six yards out.
After the game, Pellegrini said his side were the only team trying to win, but Pulis was quick to rubbish those claims
"Was that the team that cost £350 million?" he said.
"I thought our lads were brilliant and I don't talk about other teams. They gave Joe Hart man of the match so there you go."
Despite the defeat, Pulis was thrilled with his players' performance at the Etihad Stadium - where City have won all nine of their Premier League fixtures this season, scoring 31 goals in the process.
"The players went about their business very well," he said.
"We looked very solid and we looked dangerous on the break, it's just picking that final pass or finishing off the opportunities.
"Wardy gets a free header and should score but I'm being ultra-critical of the team really in respect of the effort and the way they played today.
"I'm delighted with their commitment and effort and on the break we created some really good opportunities."
The defeat leaves Palace in 17th place and outside the relegation zone on goal difference only, but Pulis is pleased with the improvement shown since he took over at Selhurst Park last month.
"It'll be tight," he added.
"We're in the group now, which we weren't when we came, so it's important that we try and get within a certain number of points of the rest of the group and it gives us a chance and that's all we can ask for."
