His behaviour was criticised by his own team-mates, who accused him of a lack of respect, but Smith was keen to move on from the situation on Friday.
"That's all cleared up," he said ahead of Saturday's trip to Aberdeen.
"He is back in the squad for Saturday's game and he was in the squad for the game against Stuttgart the other night."
Bougherra put previous indiscretions down to his daughter having a kidney infection and then having his possessions, including his passport, stolen.
But he admits, on this occasion, he put country before club and missed his flight back to Glasgow so he could celebrate Algeria qualifying for the World Cup with the country's president.
When asked if the player had offered him an explanation for his latest no-show, Smith replied: "Of course he has. Anything that happens between myself and a player is a private situation."
A return for Bougherra at Pittodrie would likely come at the expense of 17-year-old Danny Wilson, who has excelled in the heart of defence alongside David Weir in the Algerian's absence.
"These are decision managers have to make," said Smith.
"I'm just delighted we have had a young player who has been able to get a game and has acquitted himself extremely well and we are delighted with that.
"It's no problem for us. If we have to make a decision, we have to make a decision.
"We are just delighted that we've found we have a young player who can come in and play for us."
Smith dismissed reports Bougherra was set for a £4million move to Tottenham in January as "not true."
And he claimed Rangers' exit from the Champions League would not increase the pressure to offload players in the transfer window.
He said: "Everybody says you have to qualify for the Champions League, otherwise there will be drastic circumstances.
"Now they're telling you you've got to qualify for the second stage to avoid drastic circumstances.
"I don't think there is any extra financial pressure from not qualifying.
"It would have been far better if we had qualified but we haven't and I don't think it makes that much of a difference."
Defeat to Stuttgart on Tuesday night means Rangers do not even have the consolation of parachuting into the Europa League, meaning the Scottish champions will focus their attention solely on domestic issues and retaining the championship.
But Smith insisted: "That's never the way to look at it. You would much prefer to be involved on the European stage.
"That was our aim when we started out. We've not been good enough and therefore we face the consequence of not having that.
"We would much rather have it than not have it.
"It certainly clears the second half of the season but in no way does that make up for the disappointment of not having European football."
Rangers 4/5, Draw 13/5, Aberdeen 10/3