The result sees the Clarets end the midweek round of matches in 18th place in the table, but a win away to Newcastle United this weekend could see them leapfrog Watford and move out of the relegation zone.
Speaking after the draw with Wolves, Burnley boss Sean Dyche said: “I think we didn't quite find where we want to be offensively, the defensive structure of the side and mentality was excellent, to make sure we got a clean sheet, so pleased with that.
“Not offensively as strong as we've looked recently, but there's a balance and they're a good side, sixth in the Premier League, so on the whole, we wanted to win, but we'll take a draw and a clean sheet.
“We found some good moments early on, Chas (Charlie Taylor) was absolutely outstanding, going both ways, and put a brilliant ball in for Woody, who glanced a header. We started okay, but didn't really build on that and couldn't quite find our feet in the second half.
“The defensive structure was excellent, key performance from Taylor, Ben Mee solid, Nathan Collins excellent again, Lowts steady, and Popey did what he needed to do when he needed to. There was a lot of work from the side but just not with the ball as much as we'd like.”
Here is our rundown of the latest news and updates from the Premier League, as the build-up to this weekend's eagerly-anticipated action begins: