The 27-year-old netted a brace in the 2-0 Champions League triumph with both goals set up by his Chilean counterpart.
Arsenal opened their winning account in Europe's top flight for the 2016/17 season which prompted a positive response from Walcott when quizzed on the current state of the Gunners side.
"Me and Alexi are getting a good sort of partnership there," Walcott told Arsenal.com.
"But it's not just that, the whole team seems to be clicking.
"Me and Hector (Bellerin) have got a good relationship on the right hand side, it's quite a pacy right hand side.
"It's started off very well. I will look back on this game but, yeah, the combinations between me and him are very positive at this moment in time.
"We seem to sort of know when we play off each other quite well. If he comes short, I go long and we've just got a good sort of combinations."
He added: "That combination between me and Alexi is boding well."