Ings struck in the first half, his seventh league goal of the season, before Vokes doubled the hosts' advantage with his fifth in four Championship games.
Jason Shackell's own goal with eight minutes remaining set nerves jangling at Turf Moor but the Clarets held on.
"We have to give credit to Burnley because they sit top of the league and they were very good again in this one," said Adkins, whose side fell to their first defeat in seven games.
"We would like to think we can avoid the types of goals they scored but we made three substitutions after an hour and changed our shape totally in an effort to control the game better.
"It was only 1-0 at the time and we endeavoured to get something from it but Burnley worked very, very hard and I thought their front two were exceptional throughout.
"They worked very hard but I am disappointed not to have got three points because that is what we came here for.
"I thought we could have done better but when you come away from home and give teams an opportunity it obviously lifts their players.
"The place was rocking at times and Burnley put in some fantastic work."