The Magpies hauled themselves into 14th place in the table as a result of a 4-2 victory over Southampton at St James' Park, their third league win in four attempts.
Pardew later revealed he had told his players they would need to rediscover the form which propelled them into the European places last season if they were to address their concerns ahead of the first game in that sequence, a 2-1 win at struggling Aston Villa, and he has been delighted with their response since.
He said: "When we went to Villa, I said to the team, 'We have got 15 games to go, we have got to be in the top four in the last 15 games', and we are, probably.
"We have had three wins out of four in that period and that has set us up nicely for the run-in now. That's the form we have got to maintain for the rest of the season.
"You look at the Premier League table and we have now put ourselves in a position to attack 10th, and that was the importance of the victory today [Sunday].
"It wasn't about anything else for me, and that's how I tried to get the players' mindset.
"I said to them afterwards, we should attack the top 10 now, and we can with this team.
"What a considerable difference to six weeks ago it has made, the players coming back from injury and the new players."
Newcastle, fresh from their Europa League heroics in Kharkiv on Thursday night, started slowly fell behind within three minutes as Morgan Schneiderlin pounced to fire home from Rickie Lambert's knock-down.
The Magpies responded belatedly and Moussa Sissoko levelled 12 minutes before the break, side-footing home Yoan Gouffran's cross after he had made the most of Yohan Cabaye's pass.
Papiss Cisse got in on the act with three minutes of the half remaining when he blasted home a dipping 30-yard volley off the underside of the cross bar, but Lambert dragged the visitors back into it five minutes after the restart with his 100th strike for Southampton.
Cabaye restored the home side's lead with a 67th-minute penalty after substitute Danny Fox was adjudged to have handled Mathieu Debuchy's volleyed cross, and the full-back was out of luck once again 11 minutes from time when his attempted clearance hit team-mate Jos Hooiveld and flew into the net.
Pardew later compared Cisse's stunner to the goal Alan Shearer famously scored against Everton on Tyneside in December 2002.
He said: "It was a wonder-goal, an Alan Shearer-type moment, from Cisse. That's one of the goal that will certainly get into Papiss Cisse's top 10, that's for sure.
"As soon as he hit it, you sensed it was in. He has got that in him, Papiss, he can get all types of goals. But it was a really great one today, fantastic."
However, Saints boss Mauricio Pochettino was convinced Cisse's strike should have been chalked off, citing a foul on defender Nathaniel Clyne and an offside decision which was not given during the build-up.
He said: "We are very sad about the result, especially taking into account how well we started.
"But especially after we got the first goal, we couldn't really control the game as we should have.
"We went in at the end of the first half losing the game and for their second goal, it is clear that there was a foul on Clyne, and then that was followed up by an offside. That is clear on the images.
"It's not a complaint, but these are details that had an influence on the end-result of the match."