"Going behind was a blow but, as ever, they responded. I'd never count us out - we show character," said McInnes.
"Whenever we have had a bad result, and Monday was a bad result, the next game we always do well. That is something the players should be proud of."
The Perth Saints lost 1-0 at home to Dundee United on Monday evening to give them only the slimmest of hopes that they might yet finish in the top six of the Scottish Premier League.
Hearts' victory over Kilmarnock at Tynecastle on Saturday, however, put paid to that ambition.
But there was no sense of self-pity evident at Pittodrie.
"We wanted to get on the front foot and ask questions of them, which we did do. I thought we started really brightly," said the Saints manager.
"We said to the players that there was no anti-climax about this game, that it was still important for us, and that they were responsible for their own application and desire to go out there and perform."
His players, evidently, had paid attention to his words and a Kenny Deuchar header followed by two goals by Cillian Sheridan means only a freak run of results for Falkirk and St Mirren combined with a complete collapse by St Johnstone could see them relegated on goal difference.
The Saints fans, therefore, can relax, and McInnes was delighted for them.
He said: "Our fans were up here in good numbers and we have sent them home happy.
"We have a big effort with five games left and we want to win as many points as possible. We'll try to keep it going. It's important that we keep it going until the end of the season."
And on Saints' admirable efforts in their first season back in the SPL, he added: "We wanted to come and enjoy it and show people that we were good enough.
"I think we have done that. The very first game of the season against Motherwell was a gauge of the standard.
"I thought we played that game in the manner we have played the majority since. We try to be positive, we try to score goals and we try to enjoy the Premier league."
Source: BBC Sport
Source: BBC Sport