Leicester will remain second overnight with Everton, level on points with them, not playing later on Monday after their home match against Manchester City was postponed following more positive COVID-19 cases at City.
Leicester dominated the bulk of the game but failed to take their chances and missed a first half penalty while striker Jamie Vardy only came on as a second half substitute.
“We’re disappointed not to get three points and we weren’t as clinical as we have been, but it’s onto the next game,” Barnes told Amazon Prime.
“It has been a very busy schedule with some great results so we’re happy with where we are in the table.”
Leicester could have taken an early lead after Luke Thomas was fouled in the box by James Tomkins but Kelechi Iheanacho’s weak effort from the spot after a stuttering run-up was swatted away by goalkeeper Vicente Guaita.