Price has been a mainstay in the Glasgow squad since making his debut in 2015, but he's now unlikely to play for the club again after joining Edinburgh on a loan deal that surprised many observers.
While Smith insists Price's exit could prove to be a 'good decision' for all parties, he says he wanted to hold on to the experienced scrum-half.
"No, obviously not," Smith told The Herald when asked if he wanted Price to leave. "He's a good player and he's been here for a long time. But it's understandable with everything taken into account. It's a good decision in the end and we will stand by that - everyone must benefit from this.
"Obviously, I don't want to make a long story about it as enough has been said. We are disappointed to lose him, especially from my side, but there's a big picture. I've been selling a big picture to Scottish Rugby for a long time and it was an important move."
Price's departure will free up the budget to potentially bring in another player but Smith refused to be drawn on whether Glasgow had received assurances from the Scottish Rugby over a new arrival preferring to talk about the potential impact of Sean Kennedy.
"I'm going to refrain because that question falls on Al Kellock's lap. From a playing perspective, it looks like we've lost a player but we might have gained one in Sean Kennedy.
"He's been doing an excellent job for us and he was sat behind three international scrum-halves but now, suddenly, the light will shine on him again. I'm excited because I think he will do a similar job for us and we will be sure to have him during the Six Nation as he's not currently in the national frame. We will give him time to develop in that role."
Domingo Miotti's departure over the summer fueled speculation that Glasgow were keen to strengthen their options at fly-half but Smith refused to be drawn on potential arrivals.
"I'm not going to confirm or deny anything in that regard," he said. "For now, the squad is in a good position. We have a couple of cards hidden away that we can play at the right time. We'll see how the season goes and see where they are needed.
"Currently, I'm backing everyone in this group to perform the best they can and as we develop the season there might be injuries and we can decide if we are going to add someone to the squad. But for now, we are full steam ahead with the players that we've got."
Price's departure will result in more game time for Jamie Dobie who starts against Ospreys tonight. George Horne is amongst six Scotland internationals taking time off after their World Cup efforts and Smith insists the versatile back is an exciting prospect.
"He's a really good rugby player," Smith explained. "I agree there is probably a lot more continuity lurking, and I think he's still got a lot to learn. We sometimes forget that although he's played over 50 times for Glasgow, he's still only 22 years old, so he's got a lot to learn, and he's the first one to admit that being level-headed as he is.
"So, we'll just keep on chipping away by giving feedback at the end of every game and during the week, so we can see how much he can improve. He's a diligent player so I think we will see some major progress as we go forward."
Glasgow will aim to build on last weekend's win over Stormers when they travel to Wales to face the Ospreys. Zander Fagerson, Scott Cummings, Rory Darge, Kyle Steyn and Huw Jones join Horne in taking their planned rest period.
Warriors captain Steyn is expected to be out for around three months through an ankle injury but there was also concern around Jones who injured his toe against Connacht and the initial diagnosis was inconclusive but Smith has provided good news.
"It sounds very positive," he admitted. "He's got another week that we can take away from Scotstoun to get his holiday break and liberate his mind from everything that's happened. He will then come back and start his return to play almost straight away. There was some positive news and there's no further intervention needed from the medical side."