"It's something I said in South Africa I would like to bring in to start a series", Paine said.
"I'm absolutely happy with that, it doesn't bother me", said Morgan.
"Internally, we know what is right and what is wrong and that's what counts".
"Moeen and Rashid have been a great combination for us over the last few years, and today was no different".
Maintaining the theme of a new era of harmony between old rivals notorious for their bitter battles on the field, Morgan insisted England wouldn't use the ball tampering as an excuse to bait the Australians.
Banned test cricketer and former vice captain of the Australian team, David Warner, has been signed by Nine to join the commentary team for the upcoming second one-day worldwide (ODI) against England on Saturday June 16.
Asked if England would use the incident in sledging, Morgan said: "No".
Jonny Bairstow has insisted England can cope with the pressure of being the world's top-ranked one-day worldwide side as they head into a five-match series against Australia on the back of a shock six-run defeat by Scotland.
Taxi runs into crowd in central Moscow, seven people injured
An ambulance is parked near a damaged taxi, which ran into crowds of people in central Moscow , Russia June 16, 2018. Eight people were injured after a taxi rammed through a crowd near the Red Square in Moscow on Saturday.
The punishment means he can not hold any leadership position in the team for the rest of his career, but does allow him to play in overseas domestic leagues and Australian Premier Cricket - senior inter-club or district cricket competitions in each of Australia's states and territories. The Aussie skipper said that they would have to do it by their actions.
Paine expects a strong response from England, saying: "I'm sure they'll come back better for what happened in Scotland".
"We constantly need to improve our game as we go on, particularly ahead of the World Cup".
"Today they didn't. When you're defending 214 against the No 1 side in the world, you're not going to win all that often".
"We set our stall out to be number one in the world and that's where we are, whether we were number one in this game or not, Scotland would still be delighted to win, it's not just because we are number one", he added.
Australia's rookie skipper, Tim Paine will continue with the tradition of shaking hands before the game.
Coach Justin Langer has called on the team to be "number one" in professionalism, honesty and humility, and that will begin with handshakes between the sides as Australia begin a one-day worldwide series against England.