The struggling Dark Blues went down 2-0 to Neil Lennon's men to leave them nine points adrift at the foot of the table.
But they competed with the Hoops for long spells in the match and Smith insisted the display provided cause for optimism
He said: "It's not as though we were heavily defeated or anything like that.
"Looking back we gave a good account of ourselves in the Celtic match so we have every right to take confidence from that into the Aberdeen game.
"We lost to a quality side, but we have to move on and we can do so with a bit of encouragement.
"We all want to get off the bottom of the table so this game with Aberdeen can't come quickly enough for everyone concerned."
Smith knows his side are in the middle of a crucial spell with just two games left before the winter break and he is determined to give the supporters something to shout about.
Smith said: "It would be nice to round off the year with a home league win. Our fans have been so loyal that they deserve it.
"They stayed right with us during the Celtic game which the players all appreciate.
"We need them to do the same against Aberdeen and I'm sure they will. We want to give them a positive start and hopefully give ourselves something to build on.
"Aberdeen are also coming off a defeat so will be dangerous opponents. We're under no illusions about how difficult this game will be."
Winger Nicky Riley is set to return for Dundee after missing the Boxing Day defeat to his former club.
Skipper Stephen O'Donnell suffered no adverse reaction to his long-awaited comeback in midweek so is preparing to lead the Taysiders out.
The hosts are still without long-term absentees Davide Grassi, Carl Finnegan, Mark Kerr (all knee), and Jamie McLuskey (Achilles), but midfielder Iain Davidson is free to return after missing the Celtic clash through suspension.