In the second half Philippe Coutinho curled in a direct free kick and Adam Lallana added a third goal.
Middlesbrough, who thought they should have had a penalty with the score at 0-0, finished as the lowest Premier League scorers this season with 27 goals.
Klopp praised "an outstanding job" by his players in reaching the Champions League for only the second time in eight seasons.
"We had a lot of injuries and played without a lot of key players," he told Sky Sports. "To be ahead of Arsenal and Manchester United is a really hard job.
"We are Liverpool, we have to deliver but we have to improve and we will."
(Editing by Clare Fallon)
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