New manager David Moyes led the team to their first trophy of his reign at Wembley on Sunday after a 2-0 win over Wigan in the Community Shield clash and Vidic has confidence in his boss and team-mates to ensure 2013/14 is one to remember.
"People are questioning everyone," Vidic told PA Sport. "They are asking whether we can win the title again. Can we still be champions? That is not just about the manager, it is about the players as well. Can the players perform the same way as they did before? We are trying to train hard to show what we can do.
"We have a good work ethic to start with. We have trained well. Everyone wants to put themselves back into contention to win a trophy. I see the hunger. That is going to be important if we are going to win a trophy. I am pleased with that.
"Sunday was one more performance. It was another step up in form. It was important to win a trophy and it was another 90 minutes before the [league] season starts. We have slowly been increasing our form and our performances have been getting better. I am pleased with the way we played. Hopefully we can step up again against Swansea."
The Reds kick off the title defence with a Saturday tea-time trip to the Liberty Stadium, before a run of matches against the likes of Chelsea, Liverpool and Manchester City.
"It is the toughest start we have had since I have been here," added Vidic. "Obviously the first game is always important, especially when it is away. Swansea will be a tough place to go. They have some new signings. I am looking forward to