The Pittodrie side have only won once in their past seven matches and slumped to a 1-0 defeat to St Mirren in their final home game of the season.
Manager Craig Brown made a big impact on joining from Motherwell in December, lifting Aberdeen comfortably clear of relegation danger, but the team have been unable to sustain their improvement through to the end of the campaign and Smith said: "It has been a disappointing end to the season but when the manager came in the priority was to stay in the league and we have done that."
He added: "We picked up a few good results early on but the form has dipped recently.
"It is disappointing to end the season with the performances we have put in, especially the St Johnstone game on Saturday when I thought we were terrible."
Smith joined Aberdeen on loan from Norwich during the January transfer window.
The 25-year-old former Rangers left-back is due to return to Carrow Road in the summer, with Norwich looking forward to a Barclays Premier League campaign, and feels that his time spent at Aberdeen has been worthwhile.
He said: "I wasn't playing enough games at Norwich and since I came here I have got the games I was needing.
"I don't know how many games I have played but I don't think I have missed any since I got here.
"My aim when I came here was to play in as many games as I could and I have done that. I don't know what the future holds, we will have to wait until the end of the season and see where I stand."
Source: PA
Source: PA