The 41-year-old was sacked as Posh boss on Sunday afternoon after picking up just four points from the club's opening six games.
Supporters grew increasingly frustrated by Peterborough's early-season form, a run which also included a defeat to Millwall in the Football League Trophy, which ultimately cost Robertson his job.
"I can see the pressure the chairman's under, particularly from a group of fans on Twitter," he told BBC Sport. "The chairman will only make decisions in the best interests of the football club and this is one he had to make.
"At the end of the day, we are in a results business. Unfortunately results haven't been coming recently, although the performances have shown signs.
"I don't think it's the end for this team. The team can go on and do good things if they work hard enough, and have the mentality they need to be successful."
Robertson was handed a three-year deal at London Road when taking over from Darren Ferguson on a permanent basis.