On an emotional day at Sardis Road, the home side paid tribute to departing head coach Dale McIntosh in style as four tries, including three after half time, saw them to a 29-22 victory.
It was a second consecutive bonus point win for Pontypridd, leaving them in the box seat to qualify for the quarter-finals. Dicomidis was one of the scorers with Ellis Jenkins and Macauely Cook adding to Geraint Walsh's first half effort.
"We have been targeting the British & Irish Cup as a competition and we got a bonus point win last week and the same again this week," said Dicomidis.
"We've got to go away to London Welsh and London Scottish so we're not counting our chickens just yet. We'll take each game as it comes and we'll concentrate on Neath now."
Saturday's game was an emotional one for the Pontypridd squad with McIntosh taking charge of a home game for the final time before moving on to his new role as defence coach at Cardiff Blues.
"It was a fitting tribute. Chief is a massive influence on all of us and it's a great privilege to be captain for him," added Dicomidis.
"We wanted to give him the right send off as a squad and we did that with a win against a very good London Welsh side. They're top of the English Championship, they're fully professional but our boys stood up to them and we've come away with a bonus point win so we're chuffed to bits."
Dicomidis and the rest of the Pontypridd pack stood up impressively to a giant London Welsh pack and as the Premiership side prepare for life without McIntosh, the club's captain paid tribute to a man who has spent a quarter of a century at Sardis Road.
"Chief is so influential both on and off the pitch. He's not just a great coach but also a great friend and he's someone we can turn to in times of need," he said.
"It sounds soppy but it's true. He's a great bloke and we wish him all the best with Cardiff Blues. He deserves it and it's the right move for him."
Jenkins added: "It was a great send off for Chief. The atmosphere was electric, it was what he deserved and we were all delighted we could do it for him.
"We knew it was going to be a tight game with lots of kicking but we scored some great tries and matched them up front.
"The main thing was to win and the emotion was plain to see. Chief has been the biggest influence on my rugby career hands down. He's coached me since I was 13 or 14 and we get on really well. I was really pleased to play for him in his final game and a lot of the boys have said that's their favourite game in a Ponty shirt - to be part of that is very special."
In the other British & Irish Cup games to take place last Saturday, Aberavon saw their British & Irish Cup game abandoned in bizarre fashion. Opponents Bristol were ahead when a large hole appeared in the middle of the Talbot Athletic Ground pitch.
Aberavon Chairman Andrew John said: "Right in the middle of the pitch is a chamber about four feet deep where drainage lines take the surface water off the ground.
"It is a very simple and well-constructed system but this cover has failed. Whilst we have it all exposed, we are going to do a camera survey to test the rest of these lines. We will then know the full extent of the problem."
Elsewhere, Cross Keys kept up their impressive recent form as they made it two wins from two with victory over Ealing Trailfinders. Llanelli were edged out by Bedford Blues at Goldington Road.