Palmer was omitted despite Chelsea informing England that he was fit and available for selection. The decision prompted questions for Alonso ahead of Sunday's Premier League meeting with Sunderland, but the Chelsea manager said he had not discussed the international snub with his player.
"No, we have not spoken about that. We have been talking about our game on Sunday. We are very happy with Cole; I think that he's enjoying his game. He's connecting very well with the other attackers. He's helping the team.
"He's helping the team as well in developing and improving what we want and where we want to achieve, knowing that everything takes time, but I'm very happy with his quality, with his attitude, and the impact that he's having on the rest of the team."
Alonso was also asked whether he regretted Palmer missing the previous England camp, but again stressed that his priority was the player's work at Stamford Bridge.
"We have not talked about that. We are focused on our things, on Chelsea things: how to do better, how to help him, how he can become more and more influential in the game, and those are our topics to talk."
The Spaniard added that conversations with Palmer centred on Chelsea rather than his international prospects.
"We speak about Chelsea, we speak about us. We have enough on our plate. We have to focus each weekend, and that's my impact area, my control area, and what we talk about."
Alonso also provided an update on Emiliano Martínez, who has returned to training after undergoing surgery for a fractured jaw.
The goalkeeper has been working with a protective mask and could be available against Sunderland, although Alonso said a final decision would be made after the last training session.
"Tomorrow, we have the last training session before Sunday, and we will decide, but he's training. He's training well. All the decisions are tough; you know the positions, but it's very good that Emi has made a great effort to be back, that he's been, you know, ahead of the plans to be part of the team, and tomorrow we will check, and Sunday we will take the final decision."
Martínez has been adapting to the mask, which Alonso acknowledged was not particularly comfortable. However, the manager said the goalkeeper had trained with it for almost the entire week and that the medical team had given him clearance.
Moisés Caicedo is another concern after experiencing discomfort following Chelsea's previous match. Alonso said the midfielder would be assessed again, although he distinguished the problem from a fresh calf injury.
"It's a discomfort more than the calf."
There was less encouraging news regarding Maxence Lacroix and João Pedro, with neither expected to be available against Sunderland. Alonso hopes to have a clearer picture of their recoveries after the international break.
Jorrel Hato is also still some way from a return, with the manager indicating that the defender needs more time before he can be considered.
Alonso was also asked about Wesley Fofana's difficult first half in the previous match and whether he had considered substituting the defender.
He rejected the suggestion, praising Fofana's response after the break and insisting that dealing with difficult moments was part of the player's responsibilities.
"No, no, because it's about dealing with difficult moments and he did many good things. For sure, the mistakes, he knew and he reacted really well the second half he was solid."
Alonso added that he had been encouraged by Fofana's focus and maturity this season, pointing to the greater responsibility he has taken on both on and off the pitch.
Chelsea travel to Sunderland knowing that their position in the top four offers little security at this stage of the campaign. Alonso warned against reading too much into the standings, insisting that his side must continue improving and concentrate on winning each game.
"Table means not too much because that can change so much in one week. In two games, you can be fourth, so we are taking a step forward I think."
For Alonso, the immediate challenge is to maintain that progress at the Stadium of Light, while managing a number of fitness concerns and helping Palmer remain focused on his club football.