The SNP expected to get both of their candidates into the Arbroath West, Letham and Friockheim ward.
Donald Morrison, who served in the last council as an Arbroath East councillor, narrowly lost to Richard Moore of Liberal Democrats.
Alex King (SNP) and David Fairweather (Independent) were re-elected.
Mr Fairweather said: “I am absolutely shocked at what has happened to the SNP, especially Donald Morrison.
“The people have come out and made it quite clear that they want to see changes in the council.”
Mr King said the loss of colleague Mr Morrison was “a big shock”.
“There will be all sorts of discussions taking place in the days ahead, but I just don’t know what is going to happen.”
Having served around six months as the provost of Angus, Cllr King said he would be happy to put his name forward for that role.
“I would be happy to do that, but I fully accept that may not be my choice.”
Mr Moore said: “We worked the ward very hard and were hopeful.
“When I saw the first preference votes come in, I thought we had blown it but a lot of second preference votes must have come my way.
“It’s wonderful but the real work starts now.”
Result
David Fairweather Independent 1465
Alex King SNP 1206
David Lumgair Conservatives 2585
Richard Moore Liberal Democrats 326
Donald Morrison SNP 526
Turnout 45.2%, total votes 6108
