The losses resulted in the sacking of Blues boss Carlo Ancelotti, with Andre Villas-Boas brought in to replace the Italian.
And Ivanovic believes that the match-up with the club’s title rivals will show their intentions this season under Villas-Boas’ control, and give them the chance to show that last season was down to bad luck.
"Sunday's game is the first big, big test for our team under the new manager,” he said.
"It is a match which will show how far we have improved and it's even more important psychologically for both teams.
"We will all be assessing the strength of our opponents with every tackle and every pass and know we will have to use 100 per cent of our power against them.”
Ivanovic is well aware of how difficult it will be to defeat United this weekend; with the Red Devils already clocking up 18 goals in four matches and looking almost unstoppable in the Barclays Premier League.
But Chelsea were not in a dissimilar position at the start of last season, and Ivanovic knows that the Blues will have to play better than ever to get past a team with such high confidence.
He added: "United have started this season very well and Wayne Rooney is in great form at the moment.
"He has scored a lot of goals already and we will have to be at our best if we are going to stop him.
"United have clearly improved as a group this season. But we are also making progress and will look to show that on the pitch at Old Trafford.
"If you remember, we started last season in the same way as United have started this one. But it does not mean you will end up as champions."
While there is maximum pressure on the game for Chelsea, Ivanovic feels it’s a different kind of pressure to what was on the squad’s shoulders at the end of last season.
"Last season was a different situation because we went there knowing we had to win. Now we are going there just to show our best football and trying our best to get a good result," he argued.
"We always look to win every game but maybe a draw would not be such a bad result. It's very important for us to stay close to first position. We don't want the gap at the top to get too big.
"We have been encouraged by the way we have played in our last two games against Sunderland and Bayer Leverkusen.
"And we have extra motivation from the games which we lost to United at the end of last season."