Liverpool boss Jurgen Klopp hailed his team's fourth-placed finish and their total of 76 points as an "outstanding job".
Goals from Georginio Wijnaldum, Philippe Coutinho and Adam Lallana saw off Middlesbrough on the final day meant that Klopp - in his second season in charge - guided the Reds into the top four for just the second time in the last seven seasons.
The result means Arsenal miss out on Champions League football for the first in 20 years by finishing fifth, while Manchester City will join Liverpool in playing Europe's elite competition after they finished third.
"Congratulations to my team - it's an outstanding job to get 76 points," Klopp told Sky Sports.
"We had a lot of injuries and for half of the season it felt like we had a lot of key players missing. We deserve to qualify for the Champions League.
"We did the job, good and solid. It's been a long, long season.
"I couldn't imagine this morning it would be like this. We can enjoy this, congratulations to the team. We did an outstanding job to get a Champions League spot.
"To be ahead of Manchester United and Arsenal is a really hard job. We deserve it."
The pressure was mounting on Klopp's side with Manchester City and Arsenal winning until Wijnaldum struck in first-half stoppage time to ease the tension at Anfield.
Klopp' cut a frustrated figure on the touchline during the first half as his team struggled to break down a dogged Boro back-line.
However, he was unaware of results elsewhere, although he felt his players knew were winning due to the nervousness of the crowd.
"I only asked for the other results at half-time, so I had no idea," Klopp said.
"I'm sure the players became aware of it somehow. The boys delivered in a very decisive moment.
"We are Liverpool. We have to deliver under pressure.
"Everyone knows where the points are we missed. We have to improve. But for today it's a big relief."