Georgios Samaras went off with fatigue in last weekend's 2-0 win at Aberdeen after playing for Greece in midweek and Lennon will look to rest some of his squad players when Inverness visit Parkhead in the Scottish Premier League tomorrow.
Mulgrew is a doubt through illness, while Brown's muscles could not cope with the game because of the lack of training he has done as he manages a hip problem.
Joe Ledley has reported similar pain to his captain while James Forrest faces a battle to recover from a hamstring injury for the Spartak game on December 5.
Celtic face Hearts at Tynecastle and Arbroath in the Scottish Cup before hosting the Russians, when they must better Benfica's result against Barcelona in the Nou Camp.
Lennon felt his side were jaded in Lisbon, where they failed to match their previous Champions League displays, although they came within 20 minutes of qualifying for the last 16.
"A culmination of things, travelling, going away with international teams as well, it begins to take its toll," Lennon said.
"I'm going to have to use the squad for these upcoming games. We need players who haven't played as much as they would like to come to the fore and make sure our league form is consistent, so we go into the Spartak game ready to go."
Lennon, who could have Thomas Rogne back from a calf injury on Saturday, added: "It's really tough on the squad. We have probably got one of the smallest pools in the competition, the youngest, and the cheapest.
"I'm going to have to find a balance between the league and the Spartak game."