Town are currently well in the bottom half of the table and already out of two cup competitions. A strong run in the league is required now if any hopes of promotion are to be fulfilled.
"The table doesn't lie. We can argue that we've been unlucky and that we should have got some more points, but we need to start putting a run together," Groves told the Grimsby Telegraph.
"We've had an opportunity now to have a look at the division and what's about. Now it's time for us to start stringing one or two results together.
"We've been playing well, but we've got to turn those performances into results. It's time to do that now.
"We have got a reasonably settled side and the people who have come back from injury have got some time under their belts.
"We've got to start turning possession into goals, and goals into wins.
"We need to press our home advantage and we have to go for six points from these two games. It's easier said than done, but that's what we want.
"We want two wins from these games, but first and foremost we have to beat Colchester."