Jarrod Bowen struck an equaliser for West Ham after Everton went ahead through Michael Keane.
Summerville told Sky Sports afterwards: "I think it's always tricky when things like this happen and I think the boys did a really good job today to focus on the game, and I'm happy with the point we took here.
"I think the team knows me and Jarrod on the side, just give us the ball and we try our magic, so we tried to do that today, and we went 1-0 down and we stayed in the game and our guy (Jarrod Bowen), happy with the goal, so very, very happy."
On what new manager Nuno tried to implement on the night, Summerville added: "He didn't change a lot. He's been here for two days. I think we enjoyed ourselves today and I think we're going to build on this and we go on Saturday.
"I'm grateful to be back on the pitch playing and I want to show the fans and the people what I'm capable of and try to do that. I just enjoy every minute now."