The Barcelona-based club have claimed just one point from their first four games and face a tricky trip to Real Betis on Saturday.
Rodriguez is aware of the fans' frustrations ahead of the visit to Andalusia but is confident the players have the ability to go on an improved run of form to drag themselves out of the relegation zone.
He told a press conference: "Good news will come if we keep playing well. The team has changed considerably since the start of the season."
After three defeats, Espanyol finally got their first point on the board with an entertaining 3-3 draw at home to Athletic Bilbao last time out.
"The way the team is playing does not correspond with what the results say," he added.
Rodriguez feels the return of Argentinian defender Diego Colotto, who has not played for Espanyol following his summer move from Deportivo La Coruna after sustaining a foot injury in pre-season, will see them tighten up at the back.
"One player cannot change the fortunes of the squad but, on the other hand, it would be absurd to think a player of his quality would not help us improve," he said.
Espanyol boss Mauricio Pochettino and his assistant Toni Jimenez will have to watch from the stands after being sent-off in the Athletic game.
Striker Samuele Longo also saw red, potentially paving the way for Christian Stuani to make his first start.
Real Betis president Miguel Guillen placed the pressure on coach Pepe Mel this week by declaring the club should look to improve on last season's 13th-placed finish.
Mel brought in eight new players over the summer and Guillen thinks that after two wins from their first three games they should be aiming for the top half.
He told the club's website: "The results to start with haven't been bad and the manager can count on an array of players that can give more options.
"We have to have confidence. We are hoping for a better season than last year and we are convinced that we have the tools to achieve it."