The Stamford Bridge side began the match with an outside chance of catching fourth-placed Tottenham, although they required two victories and other results to go their way. But the loss consigned them to sixth place as they cannot now even catch Newcastle.
Di Matteo fielded a weakened team showing eight changes from the one which beat Liverpool in Saturday's FA Cup final but was still confident of getting a result.
Now he must beat Bayern Munich in the Allianz Arena in the Champions League final a week on Saturday in order to qualify for Europe's elite club competition.
"We have played 37 games in the Premier League and I don't think the points we lost here made the difference," said the Italian. "We have lost many points in the whole season. You need to be objective over 37 games. By utilising the strength we had I thought we would be able to reach the final and still have a chance (of the top four) with two games to go.
"But you know how demanding it has been for us - we have played every three days in the last eight weeks - and I thought a team which was energetic and fresh mentally would give us a chance. We have pushed in every game but Liverpool were better than us."