The victory, which saw Frampton take Quigg’s WBA title to add to the IBF belt he already owned, came via a split decision, despite the former having been well in control for much of the contest.
Bury-born Quigg afterwards expressed his desire for the pair – both undefeated heading into Saturday’s much-anticipated bout – to meet again in Frampton’s native Belfast.
But Frampton said: “To be honest, I would rather move on to bigger and better things.
“If I have to have a rematch, no problem, but the world is our oyster now and I think we just move on.
“It says split decision, but it shouldn’t have been. I felt like I was very comfortable in there.”
There has been plenty of talk about the winner of this clash facing Cuba’s former super-bantamweight world champion Guillermo Rigondeaux.
But Frampton and his camp are much more enthusiastic about the idea of taking on reigning WBA featherweight world champion Leo Santa Cruz.
Frampton’s manager Barry McGuigan feels that would be a “breathtaking” showdown and has labelled both a Quigg rematch and fight against Rigondeaux unattractive options.
McGuigan, who also mentioned as possible future opponents Wales’ Lee Selby and American Gary Russell Jr, the IBF and WBC featherweight world champions respectively, said: “We need to step it up to the next level.
“The money fight is Santa Cruz. The difference between him and Scott is that Scott was unsure and just didn’t want to throw as he was so apprehensive because he was being hit hard that he just didn’t want to let go.
“Santa Cruz does let go and it would be a fabulous fight.”
Frampton added: “It is very appealing to me. I think Santa Cruz could do super-bantam, but if I have to go to featherweight... I wouldn’t go to featherweight for a no-mark but he obviously is a big name.”
In terms of Quigg’s options going forward, his promoter Eddie Hearn spoke about various possible scenarios, including taking on Rigondeaux.
But Quigg himself, who only started to make a real impression when a fight struggling to live up to the hype developed into more of a battle in the final few rounds, said of a rematch: “Obviously it is the fight I want.
“The guy has just beaten me and I 100 per cent believe I can beat him, having been in there and been comfortable, then put it on him like I did in the last bit. If there was another one, I think it would take off from where we just left it.”
The 27-year-old sustained a broken jaw during the bout, which ended with 116-112 counts in Frampton’s favour by two judges, with the other giving it to Quigg 115-113.
And Quigg added: “He has got the decision, he is the world champion, he is a great fighter and I’m not going to discredit him.
“If it wasn’t for the jaw, I’d be back in the gym Monday.
“It is absolutely killing me inside, but I’ll be back. As soon as I can get back in the gym, I’ll be putting the work in and I’ll make sure it will never happen again.”
Frampton said of inflicting Quigg’s first defeat in 34 professional fights: “He may struggle to deal with it, but he is very strong-minded and I hope he can get back on the wagon.
“There are fights for him there still. It doesn’t make Scott Quigg a bad fighter to lose to me.”
As well as winning in the ring, the cacophonous noise from the 20,000 sell-out crowd at the arena suggested Frampton had the more vociferous fans.
And the 29-year-old, whose own record now stands at 22 victories from as many fights, said: “It was electrifying, inspirational, unbelievable – a great atmosphere.
“I love watching fan videos of when they are singing and stuff, and I can’t wait to watch a few back.”