McCullum was sacked from his duties of leading England in the red-ball cricket following a 2-1 series at home against New Zealand, which came after a disastrous Ashes Down Under.
The firing of the McCullum also come in the wake of the shock retirement of captain Ben Stokes with England now searching searching for a head coach and skipper for the Test side.
McCullum said: "I was disappointed, not just initially, but at the same time I fully respect the decision. We're in a results business and fundamentally our results weren't good enough. It's time for someone else to have a go.
"I don't think we got what we wanted really. Fundamentally, you want to be winning the big series. India and Australia are the marquee series and if you don't win those you haven't quite been able to achieve what you wanted to.
"I thought we had opportunities against both of those quality oppositions and we achieved some good stuff over the four years but, fundamentally, the results didn't live up to it at the back end, hence the decision was made.
"I look back on the time fondly and thank everyone that was involved in it. There has been moments where things could have turned various ways and we might be sitting here with a different discussion. You can't live in those moments, either. You're grateful for the opportunity, grateful for the relationships and efforts everyone has put in.
"For me, now it's about focussing all me attention, enthusiasm and knowledge I have of these players, the game and English cricket into the white-ball, to try to get us in a position where we're able to lift trophies and be a great representation on the field and off the field for the English fans, and for all those who support the English cricket team."
The ECB have already drawn up a shortlist for a new Test coach, and are understood to have made contact with their preferred candidates, with former England head coach Andy Flower the mooted favourite.
Brendon McCullum has been dismissed as England's Test head coach, bringing the curtain down on the Bazball era just weeks after Ben Stokes retired from international cricket.
Jos Buttler hit a swashbuckling century as England continued to dominate India, the hosts beating the visitors by 56 runs in the final game in Southampton to win the five-match T20I series 4-0.
The proposed Euro Nations Cup has encountered a significant obstacle after the England and Wales Cricket Board (ECB) declined to support plans for the tournament's showpiece match to be staged at Lord's.
The International Cricket Council has raised concerns with the England and Wales Cricket Board over the handling of Ben Stokes' international retirement announcement.
