It is tempting to want to intervene right away in this situation. Or even to confront the nay-sayers and give them an stern lecture about loyalty, teamwork, etc. But I would advise that in this situation, assuming it's still pretty early in the transition, not to go there. At least not yet.
Actions speak louder than words. Let your, and the management team's, deeds and conduct speak for themselves. Don't expect folks to trust you right away; expect and resolve to earn their trust. Through consistent, ethical, accountable behavior one of two things will (may?) happen. One, the nay-sayers may finally be won over. Or two, they will keep nay-saying but find it harder and harder to find supporters and allies for a basically unsupportable position.
Another benefit of delaying direct intervention is that you allow others on the team, junior and senior staff, to step up and counter the doubters. If someone comes to you and reports another negative comment, ask them what they think should be done. Ask them whether it's really beneficial for you to step in. Ask them what they might do. In other words, let the team work through this without heavy-handed management or using forceful measures.
And yes, there may come a point in time (and maybe you're already there) when it becomes necessary to intervene more directly. Still, the early steps will be more about inquiring rather than punishing. For example: "I understand from a number of people that you are unhappy with our progress, decision-making, etc. But I've never heard you speak these views in a management meeting. I'm wondering why you have not spoken up in those meetings or come to me privately. In any case, I want to know more about how you feel and why."
Such questions, expressed with curiosity, send a signal that dissonant points of view are welcome, but should be expressed out in the open. You also show that you're open to exploring angles that may have been overlooked.