The Newcastle boss who was a candidate for the job following Sven-Goran Eriksson's departure, expressed his pleasure at the 3-0 victories over Israel and Russia inside five days which took much of the weight off the beleaguered McClaren's shoulders.
Allardyce said: "Let's face it, the poor lad gets slaughtered for the slightest slip-up, so I'm really pleased he can go into this particular break and feel very, very satisfied with what he has achieved.
"That's not the players, that's Steve McClaren and his backroom staff, I am really, really pleased for them.
"And I am pleased for the players because they are really good players, but they have massive amounts of pressure heaped upon them from the media point of view, and I think that is one of the reasons why they under-achieve sometimes.
"But now, they are right there and they are in a great position. They have had two great wins at Wembley, so they have put that behind them now with two very, very comfortable performances."