Alonso scored the Blues's opener in yesterday's 3-1 win over the Gunners at Stamford Bridge.
Chelsea are now nine points clear of second-place Tottenham at the top of the table following the win.
But Alonso insists Chelsea aren't getting carried away.
Marcs Alonso insists Chelsea will keeping playing game by game after their win over Arsenal
"We just need to go game by game," Alonso said.
"After this win the result in midweek is an even better point so we’ll see what the other teams do and enjoy a couple of days off.
"We are working had during the week and you can see that, we are giving everything on the pitch and getting results."
Alonso ended up concussing Hector Bellerin whilst scoring his opener in yesterday's clash.
Chelsea stars meet Will Ferrell after beating Arsenal
Sat, February 4, 2017
Chelsea stars met Will Ferrell after beating Arsenal at Stamford Bridge
Chelsea FC via Getty Images
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Will Ferrell poses with Marcos Alonso and Pedro
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Chelsea are now nine points clear at the top of the table
And the Spaniard added there was no malice in the collision.
"I jumped a bit higher and got to the ball first, I didn’t even see him coming so I don’t think it’s a free-kick," Alonso said.
"I feel sorry for him, he’s a good friend but I didn’t see him.
"I hope he’s okay."