The 21-year-old forward insists the players are trying to "block out the noise" as they fight to rescue their season.
Wins over Palace and Aston Villa have given Pochettino some respite after heavy back-to-back defeats by Liverpool and Wolves. The Argentine said last night that he "doesn't care" about pressure, tension or rumours.
Palmer, who set up two extra time goals for Conor Gallagher and Enzo Fernandez, praised his boss and told Standard Sport: "The manager helps us all every day. It's just little conversations telling us what to do. He supports us massively, and credit goes to the manager for keeping us together. He has been amazing [with me] from the first day.
"When I first came in, he just put his arm around me and gave me the freedom and confidence to go out there and play — so, yes, I'm enjoying it."
Palmer went on to explain how a meeting before the FA Cup win at Aston Villa last week helped Chelsea respond to their critics. "We do have meetings and he believes in us," he said. "We believe in ourselves, but everyone will talk if you're not doing well. We just need to try and block it out and focus on ourselves.
"There's always a lot of talk, you know what football fans are like, and rightly so [that we get discussed]. Chelsea is a big club, and we've seen them win many things for a long time. If we don't get results, they will be onto us. But I think you've seen in the last two games that we are trying to stick together in our development and to keep going as a team."
The gaffer said it is all good telling us tactics, but it is down to us to show some intensity, play forward, and be brave.
Cole Palmer on Mauricio Pochettino's half-time team talk
Pochettino was dismissive of the pressure that has been building on him, saying: "I don't care about the rumours. I don't care about the tension. I don't care about the pressure. I don't care about the stresses. We know really well which is our reality and we are going to keep working."
Chelsea had just one shot on goal in the first half at Selhurst Park and allowed Jefferson Lerma to secure a deserved lead with a 20-yard strike. Gallagher equalised just after half-time as the Blues improved on a poor first 45 minutes.
"We decided we needed an intensity switch to step it up a gear [in the second half]," he added. "It was a bit sluggish. At half-time, we had a chat. The gaffer said it is all good telling us tactics, but it is down to us to show some intensity, play forward, and be brave.
"We are a close bunch of lads; we've been there for each other all season, and performances may not reflect that. You can see it in the fans, but we are sticking together. Thankfully, we got three points."
Chelsea remain in the race for Europe but must continue their momentum while 13 points behind fourth-place Tottenham. Palmer, who joined Chelsea in a £42.5million deal in the summer from Manchester City, visits his former club for the first time on Saturday.
After scoring a last-minute equaliser in the corresponding fixture, a 4-4 draw at Stamford Bridge in November, Palmer insists Chelsea can compete with the champions on their day.
"I don't know [if it will be another classic]," he added. "It will be a tough game. I look forward to returning to the Etihad. It will be strange, but I am looking forward to it and the team is looking forward to it."
After picking up his eighth and ninth assists to add to his 14 goals in all competitions, Palmer said: "I came to Chelsea to play week-in, week-out, to get an opportunity — and thanks to the club [for offering it]. I just need to keep going."