He said he was to blame for the team's season, in which they narrowly avoided Premier League relegation on Sunday.
Asked of his intentions, he said: "To win something. By the way, I shan't be selling until I do. Not at any price."
Former Newcastle striker Alan Shearer told Match of the Day that Ashley must "stop selling their best players".
Shearer added: "There was a time when they didn't sign anyone for 18 months, which is not acceptable.
"I know the city and I know the football club and I haven't got a clue what Mike Ashley is going to do. Actions speak louder than words.
"Fans are going to games out of habit, not out of hope. That has to change."
Interim manager John Carver said he hoped to remain in charge.
"From day one I've wanted this job and I still want it," he said.
After the 2-0 win over West Ham, Carver added: "The fact Mike's saying he wants to win something is fantastic.
"We've seen how good our fans are, we've seen what kind of performances we put in altogether and we all have to be together.
"If Mike's come forward then fair play to him because he wants this club to be united. It's a big, big summer for this club, we have to invest and hopefully we will."
Sunday's victory at St James' Park, which guaranteed the Magpies safety, was their first in 11 league games. They experienced a dramatic slump after ex-boss Alan Pardew left the club to manage Crystal Palace when Newcastle were 10th in the table, at the start of 2015.
"I didn't envisage us being in this position at Christmas," added Ashley, in the pre-match interview with Sky Sports.
Earlier on Sunday, former Newcastle manager Kevin Keegan told Sportsweek that Ashley "runs the club from another planet".
But the Newcastle owner on Sunday promised to "continue the policy of investing in the football club", arguing that they are on a "very sound financial footing" after a fourth consecutive year of making a profit.
Ashley added: "We may have the cart, financially, but we now need to bolt the horse on, and we are going to."
A number of fans stayed behind after the match in a protest planned by the AshleyOut.com group. It follows other demonstrations against the owner in recent weeks, which included a fans' boycott of the home game against Tottenham in April.
Meanwhile, Carver said he was proud of how his side reacted to the pressure of the occasion on Sunday at St James' Park. Second-half goals from Moussa Sissoko and Jonas Gutierrez saw the Magpies finish the season in 15th. Hull were relegated following their 0-0 draw against Manchester United.
"I think the adrenalin is still pumping, but I have to say I think we dealt with our emotions and the game very well," he said.
"In the first half there weren't too many chances and we knew it might take the last five minutes of the game before we could break them down.
"Sam [West Ham boss Allardyce] put his strongest team out and they came and were resolute, but it was all about what we were going to do and I think we put in a performance that was worthy of the victory."
Newcastle owner Mike Ashley said he will be staying at the club until they win a trophy or qualify for the Champions League.