The 67-year-old's resignation was announced on Monday night after he failed to make a single permanent signing during more than seven months in the post.
Many onlookers had suggested Kinnear's appointment had undermined the manager, and his inability to land a replacement for Yohan Cabaye during the final few days of the January transfer window left Pardew with a significantly weakened hand.
However, asked for his reaction to the Irishman's departure, the 52-year-old said: "I'm just sad to see anybody lose their job, as Joe has. He did a lot of good work here.
"But that decision was the board's decision and we have to now work towards getting us and our position in the league more secure.
"My job is actually the next game and that's what I'm focusing on."
The Magpies head for high-flying Chelsea on Saturday desperate to bounce back from a 3-0 derby drubbing by Sunderland.
But in the longer term, Pardew is planning a summer overhaul of his squad regardless of whether or not a new director of football is appointed.
He said: "That decision is the board's, but I have no problem with directors of football. In the modern game, a lot of clubs have directors of football.
"There is so much involved in transfers in terms of the other club, agents, the preparation for the bid and the finances that are involved now that it goes way past what we used to do 10 years ago.
"I'm old enough now to have been in a time when I was involved in the financial part of a transfer.
"But that part of it has gone from managers and has gone from me, I would say, for the last six or seven years for sure, and probably that's how it should be."