Sunday's Parkhead result ended the hosts' 100% run in the Scottish Premier League and took the visitors three points clear at the top.
In the lead-up to the match, the Hoops boss had appealed for 31-year-old Collum, making his debut in the fixture, to get the big decisions right.
The Irishman was still seething from last Sunday when Dougie McDonald awarded his side a penalty at Dundee United then changed his mind - and he had also pointed back to last season when he felt big decisions in two Old Firm games had gone against his side.
The former Celtic skipper claimed Ibrox midfielder Lee McCulloch, booked early in the game, should have walked after preventing Georgios Samaras going through on goal. The game was goalless when the incident happened in the first half.
After Rangers had recovered from Gary Hooper's opener just before the break to lead through a Glenn Loovens own goal and Kenny Miller volley, Collum awarded a penalty when Celtic stopper Daniel Majstorovic clashed with Light Blues' substitute Kirk Broadfoot.
Miller converted the spot-kick to seal the win but the Irishman thought that was also a wrong decision.
"I think he got a couple of big decisions wrong," Lennon said. "He has got a lot of questions to answer and I want to know why McCulloch was still on the pitch, it was blatant obstruction when we were breaking.
"It was a second yellow and they should have been down to 10 men in the second half.
"And I feel let down on the penalty incident for sure. It's a big decision. I have seen a replay of the penalty and it looked soft.
"I'm not sure he saw it and I'm not sure why he has given it.
"There was a long way to go in the game and we were trying to regroup but Daniel pulled out of the tackle and Broadfoot went down very easily.
"At 2-1 we were still in the game, at 3-1 it is very difficult for us.
"I'm not going to go on about the referee because I have my own problems with my team but you have to get the big decisions right and that's another big decision that has gone against us - and I will be asking for an explanation."
Lennon, who lost his first SPL game as Celtic boss in 17 since taking over from Tony Mowbray in March, continued: "We shot ourselves in the foot and I hope the players learn from today.
"I wouldn't mind if Rangers had cut us open but the manner of their goals was disappointing.
"But we were going to lose sometime. I just hope the players are invigorated by that for the game against St Johnstone on Wednesday."
However, the seemingly endless saga about referees is set to again dominate the agenda this week.
Rangers boss Walter Smith, who was "delighted" to win the first Old Firm derby of the season at Celtic Park, had a veiled dig at Lennon for putting Collum under pressure ahead of the game.
"I think there was unfair pressure on Willie Collum today, there isn't any doubt about that but I felt he handled the game extremely well," he said.
"We will always have arguments about one or two decisions but that's two Old Firm games out of three that the referee has been put under an unfair pressure before the start of the game.
"During all the time that I have been involved, in the majority of Old Firm games, if you look at it later on it is the best team that wins.
"There is too much focus being placed on referees at the present moment.
"There comes a time when we have to stop and look at what's happening and don't keep blaming the officials.
"We all fall out with them and have our own ideas about decisions which go against us or not but there comes a time when you look a lot deeper than that, otherwise there is no use playing the game."
Smith revealed that Sasa Papac, who had to come off at the interval for Broadfoot after a crunching tackle by Anthony Stokes after only 70 seconds, might miss Rangers' Co-operative Insurance Cup game against Kilmarnock on Wednesday night.
The Rangers boss said: "It was a sore one, right down his shin and he might miss Wednesday night's game."