The Gills, who finished 20th in League One last season, have signed eight players so far this summer.
But having started the season with a 0-0 draw to Doncaster and a 2-0 loss to Reading, Pennock wants more recruits.
"They've got to be the right players, the right characters and more importantly they've got to be good players," Pennock, 46, said.
"Everybody is pulling together in the right direction - it's a good changing room and if we can add two or three more I'll be very happy."
Although the club are still on the lookout for new additions, Pennock is pleased with those who have already arrived.
Gillingham have brought in defenders Gabriel Zakuani, Luke O'Neill, Connor Ogilvie and Alex Lacey, strikers Liam Nash, Conor Wilkinson and Tom Eaves and midfielder Billy Bingham.
"Overall, I'm happy with every single one of them - all of the new lads who have come in have contributed to what we've done, they've been absolutely first-class," Pennock told BBC Radio Kent.
"I think it's pushed the others on who were here last year as well. The whole club at the moment is in a good place."
Gillingham are looking to add "two or three" more players to their squad, according to manager Ady Pennock.