First Minister Henry McLeish acknowledged the defeat could now pose problems for the Labour Liberal Democrat pact.
The split between the two parties deepened further on Friday evening when Lib Dem Tavish Scott resigned as deputy minister for parliament because of the executive's failure to implement a tie up scheme.
The Shetland member said he had worked hard to persuade other ministers about the scheme, but had failed, and had no choice but to resign.
He described a tie-up scheme as an important part of an overall conservation package.
Mr McLeish has denied defying the will of the Scottish Parliament by ruling out a compensation scheme for fishermen to tie up their boats.
He said he wanted to find a way forward for the industry and "the bigger will of the Parliament" was to see a solution to the industry's problems.
But he was adamant the executive would not bow down to demands for a short term tie-up scheme.
Mr McLeish said: "I know there are some strong feelings about the way some of the Liberal Democrats voted. That may be an issue we have to return to.
"But for the present I want to see the industry's problems tackled first and then we can look to some of the other issues."
Mr McLeish went on: "No door should ever be closed in politics and what I have said to the industry is we need to move forward.
"That is what the will of Parliament was saying and I intend to make sure that happens.
"Tie-ups are not part of the strategy. It is a pity that in Scottish politics we get hooked on words.
"Feelings are running high about certain things that happened in that half hour yesterday.
"But for the present I want to see the industries problems tackled first and then we can look at some of the other issues."
Next week, rural development minister Ross Finnie and fisheries minister Rhona Brankin will meet fishing leaders to discuss details of the £25m package announced for the industry on Thursday.
And on Friday, a mass meeting of skippers, in Peterhead, authorised its leaders to try to renegotiate a compensation deal with the executive.
Fishermen's Action Committee leader John Buchan was cheered when he said nobody at the meeting had much time for Ms Brankin.
He accused her of listening to the industry but then not acting on what she'd heard.
The issue saw the executive suffer its first defeat at Holyrood when a four Liberal MSPs rebelled and 13 Labour MSPs, including four ministers, were not present for the crucial series of votes.
After an SNP amendment was passed calling for a compensation scheme, for tying up fishing boats and after an Executive amendment was defeated, the crucial vote was a dead-heat 55-55.
Presiding officer Sir David Steel then used his casting vote, to the fury of many in Labour ranks who argued he should have cast it the other way.
Feelings among some Labour MSPs against the Liberal Democrats were running high at conference in Inverness with one, Rhona Grant, calling the Lib Dems stupid and "cynical".
But the real issue for Labour appears to be the absence of some of its own MSPs at the crucial time.
Late on Friday, in a damage-limitation exercise, Labour spin doctors brandished a letter from Hamish Morrison, the chief executive of the Scottish Fishermen's Federation, which thanked the executive for the "handsome" settlement.
Although the letter recognised that the package would address the long-term development of the industry, it described it as an "incomplete response" which would not address the "short-run but acute difficulties facing the industry".