The Manchester United manager will remain in charge for Saturday's Premier League trip to Chelsea after chief executive Omar Berrada and director of football Jason Wilcox discussed his future at Carrington earlier in the week.
Carrick's position had come under serious scrutiny following an eight-game winless run across all competitions, with the defeat against Bournemouth leaving United just one point above the Premier League relegation zone.
The 45-year-old was visibly emotional at the final whistle at Old Trafford, but the club ultimately decided to give him further time to improve the situation.
Speaking ahead of the Chelsea fixture, Carrick was asked about the discussions surrounding his future and whether he had received any assurances from the board.
"To be honest, disappointment from the game, from the result," he said.
"It's clear from the way the game went. Dealing with that was the main thing, looking at what we could have done better. Then getting back to training with the players and preparing for the next game against Chelsea."
Asked directly whether the club's hierarchy had offered him any guarantees about his position, Carrick was unequivocal.
"I don't need any assurances from anyone; I get the position and understand the responsibility and what comes with that. I don't need any assurances from anyone."
The United manager also insisted he was not surprised to still be in charge, despite the speculation that followed the Bournemouth defeat.
"No, no, I'm here to do my job and I'm desperate to improve things. I'm not surprised, no," he added.
Carrick's comments suggest he is determined to concentrate on the football rather than become distracted by the uncertainty surrounding his position.
He also explained that he pays little attention to the criticism and speculation circulating outside the club, preferring to concentrate on the expectations of supporters.
"I don't see it really, I see the things I need to see. I don't look for it because it doesn't help.
"I care about what the supporters think, what we give them and offer them, and what they see. I know what we need to do to be better - I don't need anyone else to tell me."
United's immediate challenge is to find a way past Chelsea, with the London club occupying fifth place and sitting six points ahead of them.
Chelsea arrive following their Carabao Cup elimination against Liverpool, losing on penalties after a 1-1 draw at Anfield, while they also suffered a 2-0 league defeat against Tottenham last weekend.
Carrick, meanwhile, must find a response from a United side that has struggled to produce consistent performances this season.
The manager has recorded just two victories in 12 matches across all competitions, increasing the pressure on a team that has ambitions of competing much higher up the table.
United could fall into the relegation zone this weekend, depending on results elsewhere, making the visit to Stamford Bridge particularly important.
For Carrick, the priority is straightforward: improve the performances, restore confidence and give the supporters something to believe in.
He knows that remaining in the job is only the first step towards rebuilding confidence within the club.