Today's Hoops currently sit 18 points clear at the top of the Scottish Premier League table with 20 wins and three draws from 23 matches.
Wednesday's 4-0 victory over Kilmarnock also allowed Neil Lennon's Celtic to equal a club record 10 clean sheets in a row prompting Brown to suggest that the current crop is up there with the best Parkhead has seen.
"With this run of results and the added achievement of the clean sheets, I think this is one of the best Celtic teams in a long time," said midfielder Brown.
"So, hopefully, we can keep going for as long as possible. It's a great achievement. Looking around our dressing room and seeing what it means to the players, it shows that we have so much to play for this season.
"It was a great result against Kilmarnock. The lads played well from start to finish and I think it was played at a good tempo as well.
"We were playing one and two-touch on the pitch and we looked really good."
Celtic will be looking to extend their unbeaten streak to 24 league matches when they take host St Mirren on Sunday.
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