McClaren said: "I have lost quite a few games in the last minute and cruel endings, but never before have I felt so upset and disappointed for a set of players than I did when I walked into that dressing room.
"They didn't deserve that. They gave everything - in the second half they were magnificent. We stood toe-to-toe with a very good Everton team, and the response from the crowd was terrific, the response from the players...
"We didn't deserve to lose; we have, but that kind of performance, that bodes well for the future.
"Everton would have been disappointed if they had lost, like we are. I didn't think we deserved to lose, I thought a draw was a fair result. But this game is cruel and we have to quickly move on."
Newcastle head for West Brom on Monday knowing they will have to shake off their bitter disappointment if they are to bounce back immediately.
McClaren said: "It's very difficult, just straight away refocus and lift. They have got to recover tonight, come in tomorrow and get prepared for West Brom on Monday.
"It's a big test physically and mentally for the players after that because they gave absolutely everything.
"We talk about crawling off and they did. It was a struggle to get on the bench, they were all underneath."