We recovered from going a goal down to win 3-1 via Darren Anderton's penalty, Stephen Carr's effort from a tight angle and Les Ferdinand's late header.
The boss said: "We wanted to pass the ball, we knew it was hot and we wanted to keep possession. We then went a goal down and sometimes it is very difficult. It's hard work. The players responded very well and we're delighted."
Graham was also full of praise for an Ipswich side who more than played their part in an entertaining opener.
He insisted: "We knew it would be a tough game and they would pass the ball very well, which they did in the second half. And if the front two play like that they will give a few teams problems.
"In the second half they kept possession well and gave us problems. They were sharp and lively, the front two were mobile and gave us a few problems but we created the better chances. We also hit the crossbar and the post. Before the game I would have been happy with 3-1 though."
Quizzed as to his targets this season, Graham added: "Just two years ago the club avoided relegation so if we can get around the top six or even break into the top six, I think that would be fantastic progress."
We now prepare for a tricky trip to Middlesbrough on Tuesday.
George Graham was delighted with our opening day victory against Ipswich Town on Saturday.