While Rangers slumped to a 2-0 defeat at Aberdeen, Gordon Strachan's men completed a hat-trick of championships with a 1-0 win against Dundee United at Tannadice.
Smith now faces the task of lifting his dejected team ahead of Saturday's showdown with First Division Queen of the South at Hampden Park.
"That's what we have to do," he said.
"We have a cup final and we would like to finish the season on a brighter note than we have done over the last week or so."
Goals from Lee Miller and Darren Mackie sealed Thursday night's defeat, before Nacho Novo saw red late on for an over-the-top challenge on Stuart Duff.
The striker now misses Saturday's final but Smith had no complaints about the sending-off.
He said: "It's difficult to see from the dugout but if he missed the ball, he deserved to be sent off so I can have no argument with that."
A few weeks ago, Rangers had high hopes of an historic quadruple but an exhausting campaign, which will see them play their 68th game of the season against Queens, has finally taken its toll with defeat in the UEFA Cup final and SPL.
Being branded failures now after such an epic campaign may seem harsh but Smith admitted: "That's the fact of the matter.
"We had an opportunity to win the championship and we let it slip and that's the most disappointing factor.
"It was the failure to handle a set of circumstances that were really unusual for a team to have to handle and that's where we have fallen down as much as anything."
Aberdeen midfielder Barry Nicholson agreed a crippling fixture list played a part in Rangers losing the title to their bitter rivals.
"With the season they have had and the games they have been involved in, I think it's just been a step too far them," he said.
"They have had a lot of games to play in the last few days and the tiredness has just caught up with them.
"But they are good professionals and they will bounce back."
The clash with Rangers marked Nicholson's final game for the Dons and he is now hoping for a summer move south of the border.
But he was thrilled to bow out on a high, adding: "Rangers were going for the title so all the pressure was on them. We just had to try to enjoy ourselves and to finish fourth was brilliant for us."