Defender Andy Considine warned the Dons have no fear of any team in the bid to lift the Scottish Cup for the first time since 1990.
Aberdeen will face either Rangers or Kilmarnock in the quarter-finals at Pittodrie on the weekend of March 2 and 3.
The Reds’ opponents will be confirmed following the replay at Ibrox next Wednesday.
Rangers sit second in the Premiership table and last week defeated the Dons 4-2 at Pittodrie.
However, Aberdeen hold the upper hand this season having beaten Rangers back-to-back in Glasgow, including a 1-0 Betfred Cup semi-final win in October.
Kilmarnock are placed fourth in the Premiership table, but have defeated Aberdeen just once in the last 24 head-to-heads.
Considine, pictured, said: “We are good enough to take on anyone.
“There is no fear about facing any team and we have shown that in our league form.
“A club like Aberdeen deserves to be contesting finals. We have done that a lot in the past few years and have been very unlucky.
“Hopefully this year it can be different and it will be our year.”
Scotland international centre-back McKenna will return from a three game suspension in time for the Scottish Cup last eight tie next month.
McKenna was hit with the ban for kicking out at Rangers’ Alfredo Morelos in the loss last Wednesday.
Morelos, who stamped on the Dons defender, was also dismissed as a result of the coming together. Aberdeen accepted the red and subsequent ban, but the Ibrox club appealed.
The dismissal was upheld at a tribunal last Friday with Morelos also hit with a three-game ban.
There had been history between the two players as Morelos had been red carded for an off the ball kick-out at McKenna in the 1-1 draw at Pittodrie in August.
That red was downgraded to yellow on appeal by the SFA.
Morelos has been dismissed in all three games he has played against Aberdeen this season, having also walked early in the Reds’ 1-0 league win at Ibrox.
He missed the Betfred Cup semi-final through suspension.
Should Rangers progress past Kilmarnock, which is no guarantee, McKenna and Morelos will face off against one another again.
Having missed the 4-1 Scottish Cup defeat of Queen of the South on Sunday, the defender will also sit out the home match with St Mirren this weekend and the following trip to St Johnstone.
Considine is confident the stopper, who was the subject of a rejected bid of around £5 million from Stoke City in the January transfer window, will learn from the controversial incident.
He said: “It was one of these things in football, heat of the moment stuff.
“In sport, regardless of what sport, you have a millisecond to react.
“Whether that is a bad reaction or a good reaction, Scott is young and these things happen.
“He will know next time just to make a meal of it instead of kicking out.
“It is frustrating but that is football, these things happen and Scott will learn from it.”
Aberdeen progressed smoothly into the last eight by seeing off Queen of the South, despite being held at 0-0 by the Championship side at the break.
Considine, 31, said: “We knew Queen of the South would sit in and try to hit us on the break.
“They have some good players with (Stephen) Dobbie up front, (Lyndon) Dykes and we know Nicky Low.
“They had maybe a 15 minute spell down the right side where they were getting a little bit of joy.
“But it was nothing that hurt us.
“We knew we needed to shift the ball quicker as it was a bit pedestrian at times.
“Once the second half came along the manager mentioned we needed to up the intensity going forward, especially while also trying to keep the back door shut, which we had managed.”
The tie turned with the introduction of substitute Niall McGinn at half-time for Stevie May.
Northern Ireland international winger McGinn netted the opener within two minutes of his introduction. McGinn also set up two goals, one of them a headed effort from centre-back Considine to make it 2-1.
Considine said: “Niall came on and made the difference.
“He was brilliant and gave the right-back a torrid time in the second half.
“Niall whipped in some great balls, which resulted in a couple of goals, which was fantastic.
“It was nice for myself to get on the scoresheet again.
“We did enough to win the game but it is just about breaking these teams down.
“It is not easy.
“I can understand it is probably frustrating watching it from the side, but it is tough as a player on the pitch when they are sitting that tight and have a back five and then a four.
“We were patient when we had to be and got the result we needed.
“The bottom line was we got into the next round.”