Despite winning just one of their last nine Premier League matches, losing seven times in that stretch, Villa made sure of top flight football with victory at home to Hull City last weekend.
They fell to their 20th defeat and finished 15th with an emphatic loss at Tottenham, with Paulinho, an own goal from Nathan Baker and an Emmanuel Adebayor penalty proving the difference.
And with speculation surrounding the future of Lambert as well as owner Randy Lerner, the Scot told Sky Sports: "It's plain to see what Aston Villa's needs - there's no two ways about it. It's a massive club and the lads are hurting obviously with the criticism that's come our way.
"They've got to be proud of staying up because it's a hell of an achievement.
"It's been tough (to do my job) but it's not something I've ever shied away from and you're the manager of it, you take it on board and it's probably the greatest thing I've done in my managerial time.
"You want to stay right with. What's going to happen over the next week or two will happen. It's a shame to be where it is, but it has been like this for a few years and it's far too much for the club to be here.
"The first half was really poor. We just never got going. We were lethargic and looked like we wanted the season to finish.
"The main thing in the second half was not to lose it. We were totally running on empty, but the main thing for Aston Villa is it's in the Premier League and that was the main objective."