Dodd was disappointed with City's 1-1 draw at home to Edinburgh City on Saturday, see ElginCityTV match highlights above.
The player was drafted into Elgin's starting line-up from the bench when Ross County loan midfielder Tony Dingwall pulled up injured in the warm-up on Saturday.
The Moray side were heading for defeat when left back Jordan Allan popped up with an 89th minute equaliser.
Next up for the Black and Whites is two away games against new leaders Montrose and promotion challengers Stenhousemuir.
After that is a home game against third-placed Stirling between Christmas and New Year, before a gruelling series of games is completed with a trip to title favourites Peterhead.
"The manager spoke about these games in the changing room after the match," said Dodd. "It's Montrose next week and then we are at Stenhousemuir as well before our next home game.
"It's each game as it comes but we are aware of the run of games that's coming up.
"It's difficult and we need to try and make a statement in the next two or three games anyway."
Dodd felt let down that Elgin didn't make home advantage count against Edinburgh.
"We are looking to win all our home game particularly with what we have in mind this season, which is promotion."