The Yorkshiremen were relegated from English rugby's top flight on Saturday after a 39-16 defeat at Gloucester but showed plenty of fight and spirit despite flagging in the second half as the home team turned up the heat.
Lancaster said: "I am disappointed with the overall result of the game and we did more in it than the score says but it was our own fault.
"I felt more positives than negatives coming out of it. I thought we played very well first-half. We controlled it and played at our pace. We conceded two soft tries and going into the second half, we were confident.
"Unfortunately, we had a poor start to the second half and, ultimately, that was the difference between the two teams.
"There is no doubt that the Premiership is moving on a yearly basis. You only have to look at Gloucester, with the strength they have in their squad, and it is a big gulf between National League One and here.
"I know now that we go from everyone's underdog to everyone's favourite and you cannot be disrespectful to any sides in National League One. It is an extremely tricky league to be in and we will just work hard and try to get out of it.
"I think we have learnt a huge amount. We've learnt a lot of lessons both technically and tactically."
Gloucester head coach Dean Ryan also praised the spirit of Leeds as his side secured their Premiership play-off place with the victory, in which Fijian Akapusi Qera scored three tries.
Ryan said: "All we wanted to do today was win and get a bonus point. It was difficult and Leeds deserve enormous credit. We played well in the first half and didn't get much from it.
"We had to change tactically at half-time in that we had to be more direct otherwise we would not get the bonus point we were after.
"We did but it was a tough game for us to play in because we didn't get much from the mistake element from Leeds. They kept putting the onus back on us to play and, with a bit of drizzle and us playing fast, it was not really breaking them down."
As for Qera, Ryan joked: "He wasn't bad, was he? Seriously, though, I thought he was head and shoulders man of the match.
"Three tries sometimes come from being stood at the right place at the right time but for all his three tries, he went looking for work.
"To have him as a number seven is a great threat for us because he gets in the game and reads the game so well."