McClaren's side endured a frustrating afternoon as Aleksandar Mitrovic was denied by the woodwork and Butland pulled off a string of fine saves to keep out Georginio Wijnaldum, Moussa Sissoko and Jamaal Lascelles.
"We are very frustrated. Butland stood between us and three points," said McClaren.
"There were four incredible saves. The future is bright for England goalkeepers and I know that because I had him at Derby [County on loan]. He was excellent then and he's even better now. He got Stoke a point.
"He was excellent. Goalkeepers are there to win you points and that is what Butland does.
"We are frustrated, but the performance carried on from last week. We dominated. Important we kept a clean sheet, played good football and created chances. The first goal is always important and when we didn't get it in spells when we were on top we got frustrated.
"But we kept it going and had chances at the end. Credit to the players. We keep going like this and we will be okay. Everybody can see that the team is growing and that we are making progress. The team showed great character."
Newcastle sit 18th in the table following Saturday's results, with seven points from 11 games.