Carter Hutton started in his place on Monday and made 21 saves in a 6-1 win over the Flyers.
"Same thing for [Tuesday's] game as well. I was in a better place, but not in the state of mind that I felt that I could go out there and perform the way I wanted to," Ullmark said. "And, also, that I wasn't done dealing with the emotions and the thoughts that I had - still have - regarding all this."
After Monday's game, Ullmark was surprised when he was handed the game puck by captain Jack Eichel.
"Obviously, you don't see it coming. It was a very nice gesture. Everybody reached out to me and have been giving me their condolences," Ullmark said. "When they gave me the puck, it took all my might and my power to not break down completely in the locker room.
"We're always speaking that we have two families. We have a family at home and we have our family in the team. That certainly was one of the confirmers about how I feel and hopefully how they feel about the team."
Ullmark's father was 63 and while he was never able to see his son play in North America, he closely followed Ullmark's NHL career.
"Even though things got tough, he was always interested in my teammates, my team, and how I did," Ullmark said. "That is something I'm going to miss a lot."
Ullmark's last conversation with his dad came around the time he entered the hospital for the final time.
"I called back as soon as I found out that he was going to the hospital and he wasn't in any shape of talking or holding a phone or anything like that, but I told my mom to put the phone against his ear and I said goodbye, told him all the things I wanted to do," he said. "I'm very fortunate that I had the opportunity to do it. There are some people in the world who don't get to say goodbye and get those last words."
Moving forward, Ullmark is planning on practicing with the team on Thursday at KeyBank Center and traveling to Washington for the team's pair of games against the Capitals. Buffalo is next scheduled to play Friday night at 7 p.m. at Capital One Arena.
"You never know about these things, how you're going to feel and how you're going to handle it. But I feel a lot of gratitude towards the boys, towards the organization and everyone around it," he said. "It's been very supportive ever since they found out so a lot of love to them."