The Pittodrie side have to score at least once next week in order to reach the Europa League third qualifying round following the 1-1 first leg draw.
A penalty from Gary Mackay-Steven gave Aberdeen an early lead but substitute Sam Vokes scored what could prove a vital away goal for the visitors with ten minutes left.
“We are still in it,” said McInnes. “It is a cup tie. No one sitting here could say Burnley did not deserve an equaliser. They moved the ball better in second half. You can see why they lost only six or seven games on the road in the league last year.
“There is a feeling we can score down there. If we score down there it is game on. The onus is on us to score obviously. We won a high pressure game at Celtic Park last season in front of 60,000.”
McInnes had to hand Tommie Hoban an immediate debut at left back after Andrew Considine called in sick on the day of the game. The defender only signed on loan from Watford on the eve of the match.
The Aberdeen manager also gave 18-year-old Lewis Ferguson a competitive debut in midfield. Sam Cosgrove led the line impressively at just 21.
“A night like tonight is good for them,” said McInnes. “A lot of them have never competed in Europe.”
McInnes said he “did not care” whether commentators and observers in England were impressed with his side or not. “It probably won’t change a lot of people’s opinions. But I know where we are and how competitive we can be. We showed we are a good team – we know we are.”
Burnley manager Sean Dyche complimented Aberdeen for making it a real cup tie and noted the atmosphere whipped up by a full house of over 20,000.
“Aberdeen made it a proper, real game, the atmosphere was excellent,” he said. “When you think how the game panned out we will take the draw and away goal. We are not a side who take things for granted. We don’t think this is a done deal – absolutely not.”