Swansea boss Garry Monk warned his players their Barclays Premier League status is not yet secure despite a last-gasp 2-1 victory at Newcastle.
Wilfried Bony's double, the second of them from the penalty spot in injury-time, took the Welshmen to 36 points, six clear of the bottom three with three games remaining.
However, Monk is refusing to accept that the job is complete.
He said: "Look, I'm not going to make it up, of course the boys were delighted. But I think they realise we are not safe, we are not mathematically safe.
"It's not the point for us, the point is that we perform well in these last games and we finish the season strongly because it's been a poor season for us for the standards that we have set and we are not happy with it.
"We are not happy at all with our league position, we are not happy with the way we have been so inconsistent this season and we want to put things right.
"This goes some way towards doing it, but we have got three other games to make sure that we really finish strongly and send a message for next season."
The win was just Swansea's second in 10 attempts since their 3-0 derby victory over Cardiff in February, and they had to come from behind to claim it.
Newcastle ended their wait for a goal after six hours and 23 minutes when striker Shola Ameobi fired them into a 23rd-minute lead, somewhat against the run of play.
However, they succumbed in stoppage time at the end of either half to allow the points to slip from their grasp.
Bony did the damage on each occasion, firstly heading home Ben Davies' corner and then converting from the spot - his 22nd goal of the season - after substitute Marvin Emnes had been tripped by Cheick Tiote.
Monk said: "He's been great, Bony. Obviously with Michu having an indifferent season with niggly injuries, Bony has stepped up to the plate and you can't complain at someone who gets 20-plus goals in a season in his first season here.
"It's not just that, he's a massive character in our changing room, he works so hard every day, he pushes everyone else. If he doesn't score, he's a strength, he's a presence up front and he can be a handful without scoring goals.
"It's even better when he does add goals to it, so he deserves all the credit. He's been brilliant for us and he can only get better."
For Newcastle boss Alan Pardew, it proved another miserable afternoon at St James' Park as his side succumbed to a seventh home defeat in nine games and a fifth successive reverse for the first time in the Premier League era.
The 52-year-old, who has found himself under intense pressure in recent weeks, also had to contend with the loss of strikers Papiss Cisse and Luuk de Jong to injury before half-time.
He said: "I am low for the team and I am low for my staff. Sometimes I can sit here and say we deserved to be beaten, and in three or four of those games that we had before this, I have had to say that.
"But not today, I didn't think we deserved to be beaten today."
Pardew watched the game from the stands as he completed his touchline ban with the Magpies having won just one of the seven fixtures they have played in his absence and in severe danger of missing out on their target of finishing in the top 10.
He said: "We have had some tough games and some problems with injuries which have been manifested in the situation in which we find ourselves today.
"But I am not going to hide away from my responsibility, and I haven't, and I am not going to hide from the responsibility I have to the team because I have to pick them up after that, as you can imagine.
"At half-time, it wasn't easy - we conceded in the last minute, and we conceded a really cruel blow today. Regardless of what you think of how the game went, that was a cruel blow to concede a goal in that manner."