We took control of the first half at Goodison Park before Everton - unbeaten at home in the Premier League in 2013 - fought back in the second half.
Both teams had chances. Roberto Soldado glanced a header wide while Tim Howard saved well from Sandro, Andros Townsend and Gylfi Sigurdsson, who also saw a shot in injury time fizz just past the post.
At the other end, Romelu Lukaku just failed to turn James McCarthy’s cross on target in Everton’s best spell in the second half while Hugo Lloris, floored earlier by Lukaku, raced off his line in typical style to deny Gerard Deulofeu with two minutes remaining.
“We had a very good first half, played well and had a few opportunities to score but we didn’t create that one big chance,” reflected Lewis.
“Everton put a lot of pressure on us in the second half and credit to them, they are a good side and a lot of teams will come unstuck here.
“A draw is a good result, we’ve made a good start and we continue to look forward.”