The 21-year-old marked only his fourth appearance for the Blues in infamous fashion, coming off the bench to miss the deciding spot-kick as European champions Liverpool won 5-4 following 120 minutes which ended in a 2-2 draw.
Pulisic told the London Evening Standard: "We said to him 'It's penalties, man – somebody has to miss'.
“He's going to get his head up. Obviously it's tough but penalties are like that.
"He can deal with it and he'll be fine. He'll move on, he'll score a goal in the next game and everything will be forgotten. We're there for him."
Of his own performance, Pulisic added: “I felt great.
“To be out there with these guys… they are easy to play with. I'm happy that I can get some more minutes in and move forward with this team. I'm going to go in and give my best from the start. I want to make an impact and help whatever way I can. However long that takes, it takes but I want to make an immediate impact."