Newcastle moved seven points clear of the bottom three with a competent draw with league leaders Manchester United on Tuesday night, leaving a satisfied Pardew confident a place in the bottom three will be avoided.
But Simpson, who played his part in keeping a first clean sheet since the win at Birmingham in mid-February, does not want to think like that just yet, knowing how the teams below Newcastle still have at least 15 points to play for.
The aim ahead of Saturday's trip to Blackpool remains finishing in the top ten rather than fending off the threat of relegation. Having seen Sunderland sucked in to trouble in recent weeks, though, the right-back is keen to guard against complacency.
No, no, no, we're not safe until it is mathematically impossible for us to go down,
said Simpson. We're not expecting to go down, but I don't think we have expected to go down all season really with the group of players we have got, but we're not safe.
We don't want to be saying we are until we are, that's dangerous.
The point against United was an extra little step towards that target, it's a big point and we will go to Blackpool full of confidence looking for the win that will make this an excellent result.
Blackpool are without a win in six, losing five of those, and are in desperate need of a lift themselves having slipped in to the bottom three for the first time this season.
Simpson accepts Bloomfield Road, where Newcastle lost in their promotion season from the Championship, will be a tough place to visit, but has revealed a determination to ensure the hard work against the Red Devils.
We don't want to go to Blackpool and waste this point, he said. We don't want to make this result into a bad one by losing there. It's going to be a tough game, we went there last season and lost.
That will be in our thoughts when we go there because we didn't like that result.
They have beaten us up here this season so we need to go there and get some revenge.
They are down at the bottom and they will give it their all, but we are not easing off.
We've still got to get some more points on the board and hopefully end the season with a bit of momentum for next time.
While pegging back Man.
United to a point on Tuesday, Sir Alex Ferguson's men remain six points clear at the top of the table and on course to win the title.
It is a gap that is likely to have been extended to nine points had referee Lee Probert pointed to the spot when Javier Hernandez tumbled to the floor in the area after minimal contact from Simpson.
And Simpson, a product of the Man United Academy, said: It looked like he had pointed to the spot and my heart was in my mouth. I can't really tell you what I was thinking at the time because it probably couldn't be printed.
When he pointed I thought it was a soft decision, but then I realised he was giving the free-kick to us. I had a word with Hernandez and we're just pleased the referee was strong enough to make that decision.
He went down easily, I was going to go in, but I knew I couldn't so I managed to stop myself. He was obviously looking for the penalty. I put my arms up and made sure I didn't make much contact, if any.
He tried to make too much of it and dived. Maybe at Old Trafford it would have been given, but it would have been harsh for us because we had worked our socks off.
Simpson left Old Trafford on a permanent basis in January last year after spending time out on loan at Newcastle, Blackburn, Ipswich and Sunderland.
Born in Salford, it made the result against his former club extra special.
It was a fantastic night for me. I've spoken to a few of the players and they have given me a bit of grief, said the 24- year-old. It's just banter, nothing nasty.
This was a good point for them as well when they look at it. It was the first time I've played against my old club and my old teammates so it's nice to be able to take something off them.