Two excellent strikes from Niall McGinn secured the win and moved the Dons three points clear of Motherwell in second place in the Scottish Premiership table.
"I thought we managed the game well throughout," said McInnes, whose team had drawn their last three matches 1-1, including their previous trip to Edinburgh to face Hearts last week.
"We were very competitive, winning a lot of challenges and looking after the ball well with some real terrific play in between, creating some great chances.
"I said to the team at half-time we had to learn from Tynecastle, where we didn't show ourselves up front."
Aberdeen, who have already lifted the League Cup this season, now turn their attention to Sunday's Scottish Cup semi-final against St Johnstone and McInnes insists second place is not imperative to the club's ambitions.
"We just want to get into Europe if we can," he said. "We're not obsessed with second. We're just obsessed with keeping up a level of performance."
McGinn picked up the man of the match award after his double, but he said: "For me, the most important thing are the three points.
"After the draw (against Hearts) last week we needed to bounce back but from a personal point of view I was delighted to get on the scoresheet.
"I think we're hitting form at the right time with a lot of games coming up. It's definitely been a great season but now it's the important part of the season and we need to kick on and pull together."
Hibs manager Terry Butcher admits he still has no idea what his best side is after watching them extend their winless run to eight matches.
He said: "I am trying to find a blend and a system and a combination where they are going to be strong, we have not had that.
"We have not played well and therefore changes have to be made. I would love to be like Derek McInnes. He fields a team that is unchanged, all-singing and all-dancing.
"It is not so much as we don't know what we are doing but we are changing from game to game, not conducive to settled team. I am trying to hang onto something from previous game and I cannot hang on to a lot.
"I'm not worried about the play-off but I'm concerned that we are in a position where we want did not want to be. But I think the other teams would love to be in our position.
"We have got three of the five games left at home, and a slightly better goal difference than the others, so I'm confident we can stay up.
"Are my team up for it? That remains to be seen. I hope they are. I've got confidence in the boys that we'll get the points.
"A goal would be good. They get you points. We've only kept one clean sheet in 2014 so we need to do that and then score more than the opposition but you need to create chances for that to happen."