Huddersfield opened their league campaign with a dreadful 4-0 defeat at home to Bournemouth on Saturday - the heaviest defeat in the Football League on the opening Saturday.
The Terriers never recovered from going behind to a Marc Pugh strike after just 26 seconds and further goals from Yann Kermorgant and Callum Wilson - who scored two - left Robins fuming after the match.
"It was an absolute disgrace," Robins, who has become the first managerial departure of the new season in England, said. "We switched off and didn't play with any idea. It looked like we hadn't done anything all summer, or that we'd been wasting our time.
"That's really disappointing to me, because we worked really hard over the summer to put something together and we believe in what we’re doing. I feel let down today.
"It is the manner in which we lost today that is most disappointing. We created very few chances. It was as poor a start as we could have had."
Robins met the Huddersfield board of directors following the match and his contract was terminated by mutual agreement.
A statement on the club's website read: "Following yesterday's first day defeat, Mark met with the board of directors. At the conclusion of the meeting, Mark and the directors all agreed it would be in the interests of all parties to part company. Accordingly, Mark's contract has ended amicably and by mutual consent.
"Huddersfield Town would like to place on record its thanks to Mark and wish him all the best for the future."
Huddersfield chairman Dean Hoyle praised Robins for his hard work during his 18 months at the club
"Mark has put his all into the job over the past 16 months and has made a big contribution to the club," Hoyle said.
"He arrived at the club at a difficult time and immediately impacted to keep us in the Championship.
"Mark's approach to this has been refreshing. He has always put the club before himself and worked tirelessly on the training ground to change our way of playing and we have seen that come to fruition.
"Mark will be someone that I personally, and we as a club, will always remain in contact with."
Assistant manager Steve Thompson and first team coach Steve Eyre will take charge until the club has appointed a successor to Robins.
Robins joined the club from Coventry and was in charge for 68 games, winning 23, drawing 14 and losing 31.
The current Coventry manager, Steven Pressley, is the bookies' favourite to replace Robins on a permanent basis, with Billy Davies, Neil Warnock, assistant boss Thompson, Brian McDermott, Neil Lennon, Paul Ince, Owen Coyle and former boss Lee Clark also in the frame.