It was confirmed on Friday morning that Lawwell will retire from the club in June with Dominic McKay moving from Scottish Rugby to take his position.
Desmond showered the departing chief with praise and admitted that he did all he could to keep him at the club.
“When Peter told me he was considering retirement, I did my utmost, unsuccessfully, to dissuade him," he said. “Celtic Football Club owes a major debt of gratitude to Peter Lawwell, who has made a unique and transformative contribution to our Club. I have been privileged to work with many CEOs and Peter ranks up there with the best of them.
"Over the years, Peter was sought after by many English Premier League clubs, but his love and commitment to the Club and Scotland were more important to him. Since 2003, under Peter’s tutelage, Celtic has achieved incomparable domestic success and the number of trophies is unsurpassed by any other Club in Europe.
"Peter’s expertise and professionalism have been recognised by UEFA where he has been an outstanding contributor, to the benefit of both Celtic and Scottish football. I have had a first-class relationship with Peter over the years, speaking daily and often multiple times daily. The Club and I will miss his wisdom, energy and unwavering devotion to Celtic FC. I cannot adequately express my thanks and appreciation to Peter for all he has done for Celtic FC.”