Austin, who scored 28 goals in 40 appearances for the Clarets last season, left for QPR this week but Danny Ings' deflected effort opened the scoring at Turf Moor.
Darren Pratley's fine finish grabbed a point for Bolton but it was the Clarets who looked the more likely winners in the early kick-off.
And Dyche is confident that there is more to come from his charges after an impressive pre-season campaign.
"I was pleased with our performance, I thought it was a continuation of our good form in pre-season," he said.
"There was good energy to it, a nice solid look to it but also some real quality at times.
"We nearly scored again and that can happen at times. We're playing against a big club in terms of financial sense in this division and they will be well-fancied.
"I always want to win but the second thing you take is a good performance.
"It's definitely Danny's goal and everyone knows that he has been very sharp pre-season.
"They looked really fit and there were good signs. It (the departure of Charlie Austin) has been, it's gone and we move on.
"It bodes well for how we think the group is developing. It's one game and we've got so much still to do."