Mr Baggott said his officers had successfully dealt with an "incredibly volatile situation [...] a situation made all the more difficult by the absence of political consensus".
Police previously warned there would be consequences to the weeks of disorder surrounding Union flag protests, and the Chief Constable added: "There should be no surprises with the outcomes."
He spoke out after he met with Mr Robinson at Stormont on Monday, where they discussed a number of policing issues.
The meeting came after a number of high profile loyalist flag protestors were arrested and charged by police last week.
Each case is unique and I have not seen any unfair interpretation of the rules or due process.
Chief Constable Matt Baggott
Following the meeting, the First Minister said: "There is a perception in the unionist community that, when you see several leading republicans getting bail and several leading members of the loyalist community not getting bail, there is a lack of balance in the way that these matters are dealt with."
But Mr Baggott said police have "received very favourable feedback from across all communities regarding our measured approach".
"I reminded the First Minister that prosecutions and bail decisions are made independently by the PPS and judiciary against very stringent criteria," he added.
Mr Baggott added: "Policing does not hold the solutions alone to the current dispute and grievances which require renewed political dialogue and innovation. In this regard, I will support fully the development of the Shared Future Strategy and look forward to this with optimism."
Meanwhile a statement from the Ulster People's Forum, which has been linked to the organisation of months of flag protests across NI, called for Unionist politicians to support the weekly demonstration at Belfast City Hall.
The organisation also called for Orange Order members to "stand with their people in all areas and for the protest at City Hall on Saturdays".
Our political representatives expect support come election time and the Orange Order expect support at each parade throughout the province every parade season.
Ulster People's Forum
"For too long our people have been standing alone. The time has come for that to change."
The organisation's spokesman, Jamie Bryson, was remanded into custody last week. The 23-year-old faces charges including encouraging or assisting offences and taking part in an unnotified public procession.
Loyalist campaigner Willie Frazer, was also charged with taking part in an unnotified public procession and obstructing traffic in a public place. The 52-year-old was remanded in custody to appear in court again later in March.
DUP MLA Paul Givan said his party leader was right to raise the issue.
There are concerns, whether that's real or perceived, it's there nevertheless and that needs to be addressed and I trust the Chief Constable will be able to address those concerns over the next number of weeks.
DUP MLA Paul Givan
UUP assembly member Danny Kennedy supported Peter Robinson's claims that the unionist community has serious concerns about policing.
"I think there is an increasing perception within my constituency, from a unionist perspective, that recent decisions have been showing them considerable concern," he said.
However SDLP policing spokesperson Conall McDevitt said Mr Robinson's comments serve "only to undermine the PSNI".
He said his party will consider whether the comments are against the ministerial code and whether a complaint should be made.
"He really should reflect on how unwise he was to make political comment around operational policing. It gives the impression that he wants to direct the PSNI and that is not something the First Minister should ever do," Mr McDevitt explained.
While Sinn Féin MLA Gerry Kelly claimed there is impartiality in policing but he said it is against nationalists.
"Peter Robinson mentioned the perception of a section of the unionist community and he's probably right, it is a perception, but it's not the reality," he said.
"The reality is that the policing over this period of time was actually used against nationalists."