Lennon's side go through from the third qualifying round 1-0 on aggregate but Wilson is unlikely to advance with them as he is set to complete a return to former club Nottingham Forest.
"I would say it was Kelvin's last game for us. I don't think it (the deal) is far away," said Lennon.
"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."
As for the game itself, Lennon admitted he was glad to get through.
"It was a huge result. It is nerve wracking at this time, I was nervous all day," he added.
"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 began the game well and striker Georgios Samaras spurned the chance to settle their nerves when he put an unmarked header wide in the 12th minute.
"I felt we should have had the tie wrapped up after 20 minutes," said Lennon.
"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.
"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 will find out who Celtic will face in the Champions League play-off round when the draw is made on Friday.
Celtic are seeded and could be paired with one of five teams; Austria Vienna, Maribor (Slovenia), Shakther Karagandy (Kazakhstan) Ludogorets Razgrad (Bulgaria) or Legia Warsaw.
"We will wait to see what the draw brings, it is a step in the right direction," he added. "I am really pleased. It was a tough, tough night."