A penalty kick from top scorer Sam Cosgrove put Aberdeen in front at Pittodrie before Joe Worrall equalised to set up a replay at Ibrox on 12 March.
Cosgrove will miss that game after picking up his second booking of the tournament but McInnes is confident Aberdeen can repeat the victories they recorded earlier this season over Rangers at Hampden in the League Cup semi-final and at Ibrox in the Premiership.
“The evidence is there that we can beat them in Glasgow and the players don’t need reminding of that,” said McInnes.
“It doesn’t matter to me that we have to go Glasgow. We’ve won there already this season and our away record is very good. We’ll be alive and kicking for the replay.
“Whenever you play Rangers home or away it is tough. They’ve spent a lot of money and assembled a good side but it is important we go down there and show the belief we showed today.
“We defended very well and showed good concentration against a Rangers side which has been freescoring recently. We nullified that and Rangers’ possession was all in their own half. We carried a real threat, broke really well. We were well worth our lead and we could have had a second goal before half-time.
“We’re disappointed not to see it out from a winning position and disappointed that we conceded a goal from a set piece.”
Rangers manager Steven Gerrard, left, was unhappy with his team’s first-half performance and warned them during the interval that their season was effectively on the line.
“The gaffer told us we weren’t good enough at half-time,” said goalscorer Worrall. “He said we needed to win the second half to save our season and stay in the cup. So it was a massive goal for us. It’s my first for Rangers and hopefully a few more come along now.”
Gerrard, who unusually made no substitutions in the game, is content to get another shot at claiming a place in the semi-finals.
“I asked the players for more in the second half and to be braver on the ball,” said Gerrard. “We were better in the second half and, reflecting on the game, a draw was a fair result.
“Both teams could have won the tie today – Allan McGregor made a great save at one end and Scott McKenna made a game-saving block from Alfredo Morelos at the other end. I also felt Andrew Considine was lucky not to give away a penalty for handball but, all in all, a draw was fair.
“If Aberdeen had stayed in the lead longer, I would have looked to bring Jermain Defoe or Kyle Lafferty on but we scored and got into a good rhythm so I didn’t want to change it. Sometimes a substitution can affect the rhythm.”
Gerrard was gratified to see Alfredo Morelos, above, complete the full 90 minutes, his top scorer having been sent off three times in previous matches against Aberdeen this season. The Colombian striker did collect a booking for simulation and was generally well policed by defender Scott McKenna.
“It was another good battle between those two,” added Gerrard. “It wasn’t as eye-catching or box office as the last time, but I’m pleased they both came through the game.
“It’s nice to be talking about the game and chances rather than who is getting cited or suspended. I’m getting sick and tired with that.”