The 26-year-old and his team-mates came agonisingly close to clawing their way past Benfica and into the semi-finals on Thursday evening before a last-gasp Eduardo Salvio goal halted their late charge.
However, despite their disappointment, the Magpies have been able to take positives from their near miss - they came within two minutes of being the first team to beat the Portuguese league leaders in any competition since October - and will head into tomorrow's clash with Sunderland gunning for their relegation-threatened neighbours.
Simpson said: "That's just going to give us a big lift for Sunday, in all honesty. We have got a couple of days to recover now, but our performance and the fans and the energy and the effort we put in, it's just got us ready.
"We are champing at the bit for Sunday now. They are probably the best games I have been involved in. It just means so much to everyone. You can feel it.
"They are very special and I have been fortunate to have won a couple and drawn a couple.
"We have had a good week - we beat Fulham and had a good performance on Thursday night and were unfortunate not to go through.
"We have set ourselves up nicely for Sunday now to give it a right go and I am sure the fans will be up for it as well."
Simpson, of course, spent half a season on loan at the Stadium of Light from Manchester United earlier in his career, so he knows all about the strength of feeling on both Tyneside and Wearside ahead of a derby which has added importance this time around.
He was part of the Newcastle team which romped to a 5-1 victory over their local rivals at St James' in October 2010 and also figured in a 1-0 away win the following August.
Simpson said: "It just makes everyone so happy. It makes their night, it makes their week - it will make probably the rest of the year until the next derby.
"We know how much it means to everyone, so we are going to give 110 per cent and if we perform as we did on Thursday night, I am sure we will put a smile on everyone's faces."
Manager Alan Pardew, far from fretting over the gradually receding possibility of relegation, has set his players the challenge of securing a top-10 finish and a win this weekend would provide the perfect platform from which to launch that bid.
Simpson said: "We are in good form at the moment and the manager is right. He sets us those targets and we have got the players to do it.
"Unfortunately, we are out of Europe now, so we have got to concentrate on the Premier League.
"We have got six games left now to give it a real fight and everyone give everything we have got to try to get into the top 10."
The game will be a first opportunity for January signings Mapou Yanga-Mbiwa, Mathieu Debuchy - provided he has shaken off a hamstring problem - Massadio Haidara, Moussa Sissoko and Yoan Gouffran to sample the unique atmosphere of the Tyne-Wear derby.
Pardew has tried to tell them what to expect, but admits they probably did not understand until they experienced something of a dress rehearsal in the Benfica game.
He said: "In some ways, it was because it was an unbelievable atmosphere.
"You can only really liken it to a Sunderland game or a European game here years ago when Sir Bobby [Robson] was manager."