Austin, who was Burnley's top scorer last season, joined Queens Park Rangers earlier this week and his departure has left Dyche short of firepower.
Danny Ings took his chance to impress when his deflected effort put Burnley in front at Turf Moor, but Dyche is looking for more options.
"It's an ask for us this year," Dyche told Sky Sports when asked about the possibilities of a promotion push. "We've just lost a man who got 25 goals in the league last year.
"We're looking to use what we've got, and there were good signs there. We still want to be productive scoring wise and we are in the market to see if we can bring someone in to improve the squad."
Darren Pratley's equaliser denied Burnley an opening day win, but Dyche was satisfied with his team's performance.
He added: "I'm very pleased. We felt it was important to follow on from our good pre-season form. We had done very well, looked fit and full of energy.
"I thought for large parts of the game we performed well and there was no feeling of loss this week (following Austin's sale).
"I spoke to the players and told them we're a good group here, a very small group, but a good group. When it's so close to the season, it's not just a goalscorer but a team-mate as well, and you don't want that to affect the group.
"I thought the team didn't show any sign of that and the two up front were excellent today."