The Rams swept aside the Seasiders 5-1 in the inaugural game at the newly-named iPro Stadium to record a fifth straight Championship victory for the first time since the promotion-winning season of 2006/07.
McClaren's men fell behind to Isaiah Osbourne's early header and the visitors' goal led a charmed life for the remainder of the first half.
However, their luck ran out after half-time as a Chris Martin hat-trick, his first in the Football League, and goals from Craig Bryson and captain Richard Keogh saw the Rams romp back to win handsomely.
They were helped by Blackpool who had Neal Bishop and substitute Angel Martinez sent off, but McClaren was adamant that his side achieved the right result in the end.
"When you go behind and then dominate the rest of the first half like we did - and we played some terrific football in that first half - and go into half-time behind, you do start to wonder if it's going to be one of those days," said McClaren, who has now overseen nine matches since replacing Nigel Clough at the start of October.
"But in the second half we totally dominated and finally got our rewards, and it was probably the best 90 minutes we've put together.
"I just said to the players at half-time to keep going and keep doing what they were doing because there wasn't a lot wrong, I couldn't fault the first half.
"All I did say was I wanted them to hunt the ball better as I felt we dropped off too much in the first half, and in the second half we did that.
"It was a very good performance, very pleasing, and we need to keep producing performances like that."
The former England boss added: "With results expectations rise, and long may that continue.
"We want to play that type of football to keep the people of Derby happy and to keep them coming to this stadium."
Osbourne's third-minute goals was as good as it got for Blackpool, whose indiscipline continued as they finished the game with nine men.
Bishop was shown a straight red card for bringing down Simon Dawkins inside the area.
It presented Martin with the chance to complete his hat-trick with a penalty - the Rams striker's first goal also came from a spot-kick - and he duly obliged.
Martinez followed Bishop down the tunnel in the 88th minute for a second bookable offence.
It was the Seasiders' fifth red card in a little over 90 minutes of football following their lack of discipline in midweek at Yeovil, where Kirk Broadfoot, Ricardo Fuller and Gary MacKenzie were all sent off in the final five minutes.
It was also an eighth dismissal of the season for Paul Ince's team.