The Hoops go through 1-0 on aggregate but Wilson is likely to be back at Nottingham Forest before Friday's draw.
The Celtic boss said: "I would say it was Kelvin's last game for us. I don't think it (the deal) is far away.
"I would say he would be away over the next couple of days.
"If it is then he could go away with his head held high, I thought he was fantastic tonight for us and he will be a huge miss.
"We chatted to him beforehand, he was in the right frame of mind and didn't want to let the team down and he certainly didn't, I thought he was awesome.
"We are going to work hard to get a few players in, the players are running on empty.
"These qualifiers are tough and we have two games to go before the group stages."
The draw for the play-off takes place on Friday where the Parkhead club will take a step closer to the lucrative group stages of the competition from which they emerged last season to reach the last-16 of the competition.
Lennon said: "It was a huge result.
"It is nerve wracking at this time. I was nervous all day.
"It was a tough night, we showed great character.
"It was a tough game and you have to give credit to Elfsborg, they gave it everything."
Celtic started the brighter and Georgios Samaras could have doubled their aggregate lead with an unmarked header in the 12th minute but Lennon was pleased just to see his side advance.
"I felt we should have had the tie wrapped up after 20 minutes. You would expect him (Samaras) to score or get it on target anyway and then their goalkeeper has made a fantastic save from Joe Ledley," he added.
" We only needed the one goal to burst the enthusiasm of Elfsborg.
"We became a bit scrappy but with a bit more quality we might have picked them off near the end.
"My back four were wonderful and we restricted Elfsborg to minimal chances."
Lennon added: "We will wait to see what the draw brings. "It is a step in the right direction.
"I am really pleased. It was a tough, tough night."
Elfsborg boss Jorgen Lennartsson conceded that the best side over the two games went through.
He said: "We are disappointed of course, we were the better team in this game.
"We were defensively good anmd we created some chances but we didn't have the quality in the final third to score.
"We pushed them all the way but of course Celtic were the better side in the first game and if you take the two games together, they deserved to go through."