The Foxes ended a five-game losing run which saw them slide into the relegation battle as Barnes' goal secured a 1-1 draw at Brentford.
"Every game is going to be important going forward now," Barnes told LCFC TV.
"We play a lot of teams around us over the next month or so, so they're going to all be big games.
"They're all chances for us. They're six-pointers really. You beat them and you see yourself looking up the table. There's probably eight or nine teams now who are in the fight.
"We've got to aim to top that mini-league and get ourselves out as far away from the bottom three as we can, as quickly as we can as well. That's important. Hopefully we can go on a good run after the international break.
"We'll get everyone back fit and healthy and have a good, strong finish to the season."
Brentford led through Mathias Jensen's deflected strike, but Barnes raced on to James Maddison's through-ball to snatch a point.
Denmark midfielder Jensen is enjoying a fine season after a stop-start campaign last year.
"Matty is a very good player - he's been brilliant for us throughout his stay at Brentford," said Bees boss Thomas Frank.
"Last season he had a very disruptive season - small injuries, I think he had Covid, I think he was ill. All that got him out of rhythm.
"This season he came back in a top place and he's just carried that on from there."