The Ibrox outfit cut the gap to nine points with Sunday's win.
"We have six very important league games and it's important we go right through the line this season," Dons manager McInnes told BBC Scotland.
"Hopefully a Hampden cup final and finishing in second spot - I firmly believe that we will do that."
The Pittodrie side, who face Hibernian in the Scottish Cup semi-final on 22 April, went into Sunday's game having won 10 home league matches in a row.
Rangers shaded the first-half chances but the hosts were well on the front foot when Kenny Miller scored the visitors' opener after 79 minutes. The striker added a second two minutes later and substitute Joe Dodoo made it 3-0 in 83 minutes.
McInnes admits he was taken aback by the sudden turnaround and was disappointed by the manner in which his troops responded.
"I think we had real control of the game," he added. "I thought we were better team, certainly in the second half. We started both halves really well but we allowed the first half to get a bit untidy and we didn't pass the ball the way we normally do at home.
"We started the second half strongly and the game was played in their defensive third. Their keeper made a couple of very good saves, particularly from (Adam) Rooney - I thought it was past him to be honest.
"When I was contemplating changes at 0-0 I didn't feel a threat and I thought the goal was coming but unfortunately for us we played a part in our own downfall by giving away a poor goal and we had a crazy five minutes after that.
"Our reaction to losing the first goal was what I'm most disappointed with. From being in charge of the game and looking the most likely we've allowed Kenny Miller the opportunity to show his quality, and he showed it.
"Mentally we've got to be better than that. We normally respond well to going behind - it doesn't happen too often but we have to react better than that and if there's one lesson from today, it is that.
"It's a sore one for us, no doubt about it. In the eyes of our supporters that's a huge disappointment today and we understand that.
"We lost the fight today but it's important we still win the battle for second place, and hopefully get ourselves into a cup final
"We've been on a very good run but that doesn't give you any guarantees, and it's a reminder that there is still work to be done. When you lose a game like today and the huge feeling of disappointment, wishing we could play it all over again, we've got to channel that the right way. We have plenty to look forward to."

HebCelt is taking place in Stornoway and will run until Saturday night.
This year's acts include The Waterboys, Imelda May, Lucy Spraggan and Skerryvore.
Also, the Peatbog Faeries and Dougie MacLean.

Nearly a third of those making applications wanted to put all their debts in one place, a survey for Lloyds Bank suggested, with another third wanting to buy cars and bikes.
It said 84% of borrowers were confident about making future repayments.
Debt charities urge debtors to budget for interest rate rises.
People should also consider how they would repay were they to have a significant change in their life, such as the addition of a child or the loss of a job.
Lloyds said that while major purchases might prompt loan applications, there was a fall in the share of loans used to fund home improvements.
It added that borrowers were more confident in the second quarter of the year than the first when it came to making repayments on unsecured loans. The proportion rose from 81% to 84%.
The bank said that this signalled that people were increasingly "in control" of their finances.
Many analysts have warned that this confidence could take a knock when the Bank of England raises interest rates.
Such a move could come as early as the start of the new year.
Derek McInnes is convinced his Aberdeen side will finish second in the Premiership, despite their 3-0 home defeat to third-placed Rangers.
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Music fans are gathering on the Isle of Lewis for the annual Hebridean Celtic Festival.
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Borrowers are applying for personal loans mostly to consolidate existing debt or to buy cars and bikes, a lender has suggested.