Three goals in 15 first-half minutes for the north east outfit ensured Boro secured a top-half finish in the Sky Bet Championship and ended the season on a good run of form.
On-loan strikers Danny Graham and Lee Tomlin were both on target while Emmanuel Ledesma notched a brace.
Karanka said: "I'm very pleased because I said before the game that it's not the same to finish the season winning or finishing the season losing, so I'm happy with my team.
"We have finished winning six out of the last eight games and I'm now thinking about next season.
"I think today wasn't a real test because it was difficult for Yeovil to play because they were relegated last week and playing at home. But for us it was good as players like Danny [Graham], Tommo [Lee Tomlin] and Manu [Emmanuel Ledesma] finishing the season scoring goals.
"The most important thing for me is the team and the team is built. All the players showed me this season they are a good team and are very professional, and with these players and one or two more we can do better next season.
"I'm happy because the most important thing is how happy our supporters are. I came here five months ago and they have always been supporting us and helping us. If the people are happy it's because our work is good."
Yeovil Town will return to League One next season after a one-year stay in the Championship.
Manager Gary Johnson was forced to sit in the stands after being hit with a one-match touchline ban during his side's defeat at Charlton last month.
Johnson said: "I was disappointed with the performance but that's the nature of this league and if you don't compete then teams can cut you open. Unfortunately maybe some players had their eye on somewhere else.
"We defended poorly and generally we don't make those mistakes and misjudgements, but that's how it went today and we couldn't get ourselves in the game.
"It's gone and supporters have enjoyed the season, but we're sorry they have a poorer feeling today than if we did give it a go.
"I've had 850-odd games and not once have I been in front of a disciplinary panel but the linesman decided to report me at Charlton and once you're reported you've got to go and fight your case.
"I fought my case but got a one-match ban which was today, and I felt it was better to see it out at the end of this year rather than the beginning of next season."