England began its campaign with a poor showing in a defeat against France in Paris before grinding out a victory over Scotland amid tough Edinburgh conditions in round two.
England had come under scrutiny following a mixed start, while coach Jones was initially questioned and subsequently vindicated for his decision to move centre Jonathan Joseph to the wing and continue with flanker Tom Curry at number eight.
"It's pressure from everybody else, not us," England captain Farrell said when asked about the outside voices.
"We're unbelievably happy with how things are in-house. We feel we are getting better and couldn't wait to play this game.
"I think you saw that from the way we started the game. It's nothing to do with anyone on the outside. We are giving ourselves lots of confidence to rip in come kick-off."
England were boosted by the return of powerhouse centre Manu Tuilagi, a player Farrell feels would make a difference to any team in world rugby.
"You don't need me to tell you [how important he is]," Farrell added.
"Any team in the world would want him by your side, we're lucky to have him. He's playing brilliant rugby."
England led 17-0 at the break with George Ford and Elliot Daly the beneficiaries of some shoddy Ireland defending, while Luke Cowan-Dickie touched down from an England drive in the second half.
Part of England's success owed to their dominance of the forwards, with the returning Courtney Lawes earning the man-of-the-match award.
"We knew Ireland were on good form and we came out flying, we put an emphasis on that all week. It was great to get out here with the boys," Lawes said.
"Any chance I get to put on the shirt, especially at my old age, I relish it. We just want to keep building, the goal is to be the best team the world has ever seen."