"There is no doubt in the squad and we still believe we can go on and win the Championship," said Warburton.
"We have three away games and it is looking like an uphill struggle but we have to believe in ourselves.
"We're very disappointed to start with a loss but we have to stay positive because we're more than capable of going to Scotland and getting the win.
"There are four games left to play for. I don't think anyone is going to win the Grand Slam and it is a pretty level playing field."
Warburton believes despite failing to secure the victory there are still plenty of positives Wales can take into this weekend's clash with Scotland, who themselves suffered defeat on the opening weekend.
"I look around the squad and I feel privileged to be a part of it. With players like Shane and James Hook our back line looked awesome at times against England," he added.
"It's the same for us all the time - silly little errors. We need to be more clinical in attack and build the scoreboard.
"We've got to get back together and train hard. The mood has been very good over the last couple of weeks and we don't feel that far away.
"Scotland's back row was outstanding last year and hopefully we can nullify that threat. We're playing well in patches when we were offloading and keeping the ball but we have to be consistent.
"We have to play with our heads up and not stick to a three-phase plan if we see something is on. If there is an opportunity we have to take it."