Liverpool boss Brendan Rodgers branded substitute Markovic's red card "an awful decision".
Markovic was dismissed after pushing his arm out in the direction of Behrang Safari, but he did not appear to make contact, with the Basle player falling to the ground.
“I thought it was an awful decision,” Rodgers said. “I thought the referee was disappointing on the evening to say the least.
“Markovic came on and was bright, made a difference to the team, he was dynamic.
“He had just taken a touch away, he’s obviously got his arm up, but if that’s a sending-off you are going to have two or three sendings-off every single game. It was a really, really poor decision.
“I’m not even sure whether the referees have seen it, but I think he’s seen the player hold his face and lie down, but there was no way that was a sending-off.”
On going out of the Champions League, the Reds boss added: "We now have to fight going forward to be in it next season and obviously our performance level needs to improve over the course of the season."
Captain Steven Gerrard also acknowledged the red card proved a key moment. “We knew if we were still in the game with 20, 25 (minutes) to go, if we could get that goal it would have been hell for Basle,” he added.
“Unfortunately we just never had enough energy, enough legs in the last 15, 20, because the referee has sent him off. “I haven’t seen the incident, but I’m told it was very harsh.”
Liverpool, without the injured Daniel Sturridge, have struggled for goals this term. Gerrard added:
“What’s crucial is that we try and get our main striker back who is capable of getting us the goals to get us into the top four.
“We need to try and get Mario Balotelli back firing as well. If we can get goals in the team it gives us a better chance, but at the moment it’s a bit of a roller coaster, it’s tough.”
