"Teams know us more than they did last year. They know the way we play," Gutierrez told BBC Newcastle.
"For players that come in it's always difficult in the second season."
Last season's start was vital to a Premier League tally of 19 wins in 38 games, after Pardew's side went unbeaten in the first 14 matches in all competitions.
"Maybe we are not at the same level last year in the league but we have another competition now, and it's always difficult," Gutierrez added.
"Teams who aren't normally playing in Europe and don't have a big squad can find it difficult to play in an extra competition.
"It's our first year, it's something new, but the whole team is thinking about that and trying to enjoy it, everyone wants to play. But it's made the beginning of the season tougher.
"The win against West Bromwich Albion last weekend was really important to take the points at home."