Alan Pardew vowed to battle on as Newcastle manager after being subjected to a torrent of abuse despite seeing his side end its six-game losing run.
The Magpies beat Cardiff 3-0 at St James' Park to secure their first win since March 22, relegating the Bluebirds in the process.
However, the game was played out amid a tense atmosphere as home fans, several hundred of whom walked out at two pre-arranged points in the second half, aimed chants at Pardew and owner Mike Ashley.
The 52-year-old, who was booed by a section of the crowd whenever he stepped out of the dug-out, chose not to join the players on the pitch after the final whistle, but he is refusing to be bowed.
He said: "I am frustrated a little bit, of course. Some of the criticism has been a little bit left-field and a little bit over the top, and that's fuelled the anger here.
"You have to accept that, unfortunately, when you lose six as a Newcastle manager.
"They are upset, they are angry - I understand that. I apologise to them for the last six games and hopefully, we have taken a very, very small step towards them.
"Coming to the sideline, I was only antagonising them and I don't want to do that and make the atmosphere worse for the players, so it made a lot more sense to let [assistant manager] John [Carver] do that and take a seat."
Newcastle supporters repeatedly sang Hatem Ben Arfa's name with the midfielder among the crowd after once again being left out of the matchday squad, and Pardew was forced to dismiss social media rumours that the pair had come to blows.
"I have seen that. It's an absolute load of rubbish. He came and shook my hand at the end and that was it," he said.
On the pitch, the Magpies took the lead with 18 minutes gone when, after Cardiff 'keeper David Marshall had denied full-back Mathieu Debuchy twice in quick succession, Ameobi headed home Moussa Sissoko's cross for what seems likely to be his last ever goal at St James'.
But they were unable to build upon their lead and the visitors gained the upper hand after the break, and had it not been for a fine save by Tim Krul, who had already kept out Wilfried Zaha's first-half effort, and a goal-line clearance from Fabricio Coloccini, they might have been back in it.
But Cardiff's hopes finally died as time ran down as Loic Remy stabbed home his 14th of the season and substitute Steven Taylor made it 3-0 to end their survival hopes.
Pardew will head for title-chasing Liverpool on the final day knowing even a win there might do little to improve his standing on Tyneside.
He said: "You have to be resilient in the modern day. We have lost half the Premier League managers this year - we might even lose another four or five in the summer.
"It is sometimes a thankless task. It was difficult today, I'll make no bones about that."
Opposite number Ole Gunnar Solskjaer left St James' knowing his team will be playing in the Sky Bet Championship next season, but he was in equally defiant mood.
He said: "You have just got to face the facts, don't you? I face it head-on. I knew what I was coming into.
"I didn't make the impact I hoped for and I believed in, but that will be something for me to chew on now for a little while.
"I am a warrior - I might not look like it here where I'm sitting, but I have had times in my football career when I was a player that were very disappointing.
"You have just got to stand up and fight for yourself and fight for what you believe in."