Chelsea came alive after the interval with two goals in eight minutes, the first a Salomon Kalou header set up by Alex's astute nod across the face of goal.
He said: "This is my first game and I though the attitude and desire of the players to give their best was very good.
"You won't hear from me that the team is not good enough to stay up.
"We know we have a lot of work to do and we know that work must begin on the training field.
"Nothing I saw today changed anything. The scale of the task I had envisaged hasn't changed.
"I didn't come here naively and wasn't appointed naively. As a result we must get on and do what needs to be done.
"If there are players available in the transfer window that we think would make us better now and in the longer term then we would be interested."