McClaren was public enemy number one with England fans who called for him to be sacked before and during the previous group clash with Andorra in Barcelona in late March.
The negative response towards the England coach was put to one side as the first full international at the new Wembley saw a creditable performance in a 1-1 draw with Brazil.
But Gerrard knows England have still to turn the corner completely and he insisted McClaren was the right man to lead their attempt to reach the finals in Austria and Switzerland.
The Liverpool captain said: "There's no getting away from the fact the performances in the few games before Brazil hadn't been to the standard we'd wanted.
"We all know the ability is in the squad but this team has got to show it on the field.
"This team has got to prove to you guys (the media) and the supporters that we are a good side - and a consistent side."
Gerrard added: "To be honest, Steve has been good since he took over. As a player, I'm one of the more experienced players now and the criticism he took was unfair because he had been doing everything right.
"He was preparing us right and telling us the right things and he believed in us as players.
"At the end of the day, I believe a manager can only do so much. The players have to do the main part of the job on the pitch.
"Don't get me wrong, he's the England manager and stick comes with the job. Stick comes with any manager's job. But it's no good us as players hiding behind that. We can't just think it's all right because the manager's taking all the flak.
"We've got to get out there and take the heat off him. We are the so-called best players in England. We're getting picked to go out there and do a job. It's down to it well."
Gerrard added: "Have England turned the corner? Not just yet. I don't think, after one good performance against Brazil you can say, 'Everything's great, everything's going to be fine, we've turned the corner.'
"We've got to prove it over a long time. We've got to go and beat Estonia and move up this group.
"Then we can sit down once we've qualified and say 'Listen, it hasn't been great but we've done the job and qualified'. Then we can go and prove to people we are a good team by doing well in a tournament."
Gerrard admitted the clash with Andorra was one of the toughest of his distinguished career before his two goals helped earn a 3-0 win.
He said: "That Andorra game, believe it or not, was one of the hardest international games I have ever played in.
"Why? With the supporters against us and because you were just playing against a side who had no ambition at all to cross the halfway line.
"I don't like situations like that but I think it has to bring the best out of you. I think the experienced players had to stand up otherwise you end up drawing a game like that 0-0."