Kittrick was dismissed by the Seadogs following the 2-1 defeat at home to Stalybridge Celtic last weekend, which left them four points off the play-off places, after three years in charge.
He said: “Having taken a few days to absorb the boards decision, I thought it only right to break my silence by thanking the players and most importantly the incredible fans who have been a massive support during my tenure at the football club.
“I have thoroughly enjoyed my time at the club and know that I leave it in a much stronger position than when I took over, both on and off the field.
“It has been some journey! Having inherited a squad with a remit of survival in my first year, to reaching cup finals, play offs and promotion in our homecoming year. Great memories that I am proud to have shared with the fans.
“The decision to relieve me of my duties has come as a shock. I understand that recent results have not been what we have grown to expect from this team, however, with 7 games left we are still in the hunt for the playoffs and our target for this season is still very much alive, along with a cup final to look forward to.
“I wish the club, its fans and all associated with Scarborough Athletic all the very best for the future.”
Scarborough begin life after Kittrick with a tricky trip to Buxton in the EVO-STIK League Premier Division on Saturday.