Cole's fifth-minute effort was cancelled out by Shola Ameobi on the stroke of half-time. Alan Shearer hit a long-range winner for Newcastle after 48 minutes but John Terry struck the inside of a post in injury time.
With the title race mathematically over, Ranieri will now try to hold off Manchester United for the runners-up spot and overturn a 3-1 first leg deficit against Monaco in the Champions League.
"It won't be easy to finish second because we have go to Old Trafford but I am pleased with the spirit of the team," said Ranieri.
"I said four matches ago after Arsenal beat Liverpool that they were champions. Well done to them, the difference between them and other teams is that even when they don't play 100 per cent, they win matches.
"I think we are very close to them but of course they have more experience after coming close last season."
Cole's goal had been long overdue but he denied it had put him under any pressure.
"I go out to enjoy playing football, I don't have anything to prove to anyone," he said. "I had scored a couple of cup goals for Chelsea and one for England. What gives me most enjoyment in the game is winning matches."
