The winger scored his first goal since August 2012 to help clinch a 2-1 fifth-round win over Leicester on Sunday.
It was in front of watching new manager Tim Sherwood, who replaced Paul Lambert on Saturday.
Victory moved Villa into the last eight for the first time since 2010 and Sinclair believes the competition is wide open.
"It is getting to that stage where any team can beat anyone on any given day," said the Manchester City loanee.
"All the teams that are left will be thinking they've got a chance to get to the final.
"We have a chance as well but we will have to see who we get in the next round."
Sinclair scored a hat-trick at Wembley when Swansea beat Reading 4-2 in the Sky Bet Championship play-off final in 2011.
And the 25-year-old would love a repeat should Villa make it to the national stadium.
"That would be perfect, it would be great for me to get there and score another hat-trick," he said.
"It has been very difficult for me over the last 18 months to two years but I keep on going and hopefully if you work hard you get rewards.
"I feel sharp
It is just about getting the awareness and everything else back
I haven't played for a long time so it's just about getting my form back."
Matt Upson admitted Leicester's mistakes cost them as they struggled to recover after Villa took the lead through Leandro Bacuna.
Andrej Kramaric scored an injury-time consolation, just a minute after Sinclair's key second, but defeat leaves the Foxes with just league survival to focus on with the side bottom of the Barclays Premier League.
"We were tested in the first 10 or 15 minutes and didn't really get a foothold in the game but then we got into it, grew into the game and started to get a bit of the ball," Upson told the club's official site.
"It's difficult when you've got a player with Christian Benteke's athletic and aerial ability, but I think we shaped up quite well.
"We coped with his knock-downs and second balls that were always going to come from him
"I think whenever you concede a goal you'll be disappointed but having looked at both the goals, there are two or three small choices or tactical decisions that maybe we can look at, work on and improve as a team
It'll hopefully make us a bit more solid."
Source : PA
Source: PA