The Tynecastle side were docked 15 points at the start of the season for breaching insolvency rules, with several bookmakers installing them as favourites to finish bottom of the table.
Two wins and a draw from their first five games have seen Hearts reduce the gap separating them from second-bottom St Mirren to nine points. Walker has said that the club's critics have made the players more determined to succeed.
"It was a massive inspiration for us. Everyone was against us, the odds in the bookies were against us. Everyone thought we were going to go down," Walker told STV.
"But we've had a good start. We had some hard games but we've done well and everyone is buzzing ahead of Saturday. Now we want to prove the people who doubted us wrong.
"There is still a massive gap to St Mirren and we know it is going to be hard but we believe we have the quality to do it."
Hearts face Celtic on Saturday.