However, Sturrock - whose side have dropped to 19th in the table, three points above the drop - insists he will stay at Home Park and said: "I'm here until I'm told otherwise. I intend to be here for the long haul and as I've said before, I'm up for the challenge because I knew that this season it was never going to be easy.
"I have not been relegated before as a manager and don't intend to be now. We have got to turn things around and I am sure we can.
"Three of our next four games are at home and we have the opportunity especially if we play like we did in the second half there tonight."
Opposite number Neil Warnock saw his side move up to 13th and end a four-match losing streak and was gladdened by the quality of the Eagles' performance.
"That's the best I have seen us play for a long while, possibly the best since I have been here," Warnock said. "Our first-half performance was super and we got three quality goals.
"We knew we would have to come out of the traps quickly and we did that. I was delighted."
The former Pilgrims boss added: "It was just a shame for Plymouth that we were at our best, certainly in the first half tonight.
"I feel for Paul because you could not say that one of his players tonight did not give their all.
"I gave Claude Davis his debut and he did well for us.
"We were like Plymouth and had not win since Boxing Day and I feel sure that Paul will turn it around here. You just have to get through it - and they are good enough."
Argyle started well with Alan Judge's free kick needing to be palmed away by Palace keeper Julian Speroni.
Recalled Argyle left back Gary Sawyer made a brave block to deny John Oster but two minutes later the visitors went ahead.
Oster's deep cross from the right was headed home at the far post by Neil Danns, who looped his header over home keeper Romain Larrieu in the 21st minute.
Seven minutes later and Palace went 2-0 up.
Sean Scannell's thumping low drive from the right side of the penalty area was tipped on to the post by diving Larrieu, who could do little as the ball rebounded off the woodwork to Palace striker Alan Lee, who side footed home.
Argyle - whose last win was a 2-0 victory over Southampton nine games ago - did their best to reduce the deficit but another lightning break from Palace resulted in them forging further ahead.
Oster finished superbly, sending a low angled drive from the right side of the penalty box past diving Larrieu.
Sturrock sent on all three subs in a bid to turn the tide and in the 68th minute, after having an earlier penalty appeal turned down, finally scored.
Left-back Sawyer roofed home at the far post as substitute Paul Gallagher's pacy cross from the right was helped on by skipper Karl Duguid.