"Edwin Poots leaves Unionism in a weaker position than where he found it", Mr Allister said.
After Arlene Foster's resignation as First Minister on Monday, the DUP and inn Féin had just seven days to nominate for the two positions, or else power-sharing would collapse.
Early on Thursday morning, a deal was reached, with Secretary of State for Northern Ireland Brandon Lewis declaring that legislation would be brought in by Westminster by October if not first introduced at Stormont.
Serious question marks now hang over the future of newly appointed First Minister Paul Givan, who was nominated alongside Deputy First Minister Michelle O'Neill on Thursday.
There has been several weeks of discontent within the DUP culminating in much dissatisfaction in the nomination by Minister Poots, of Paul Givan as First Minister this week.
Therefore, the Sinn Féin party will fully participate in the executives of the five parties, McDonald's said in a statement, paving the way for Giban to become the first minister.
USA to donate 500 million Pfizer vaccine doses globally
Officials say a quarter of the nation's excess will be kept in reserve for emergencies and for the U.S.to share directly with allies and partners.
The agreement includes Irish-speaking rights, and Sinn Féin leader Mary Lou McDonald refused to do so in Belfast after the British government passed the law in the London Assembly.
A deal was agreed with the United Kingdom government to legislate for Irish language laws, as agreed in New Decade, New Approach, if Stormont does not.
On Friday night, the Loyalist Communities Council, the umbrella group which represents unionist paramilitaries, called for the next DUP leader to "stop the constant flow of concessions to Sinn Fein even if that means suspending the normal operation of devolution".
Perhaps the most reassuring part of all this is that if you think you aren't very good at your job or are lacking in confidence, then at least you can say you lasted longer than a leader of a political party in the UK.
"This has been a hard period for the Party and the country and I have conveyed to the Chairman my determination to do everything I can to ensure both Unionism and Northern Ireland is able to move forward to a stronger place".