Championship victories over Plymouth, Scunthorpe and Peterborough in the space of a week saw Forest climb to 10th spot and within one point of the play-offs.
Tyson told BBC Radio Nottingham: "A lot of us would want to achieve a lot more than just reaching the play-offs. Everyone's buzzing but we need to keep the momentum going."
With the Reds in form and in their highest league position since reaching third after seven games of the 2003/04 campaign, there is a sense of expectation that they could mount a serious promotion challenge.
However, boss Billy Davies has consistently stated that he pays no attention to league standings at this stage of the season and is eager not to get too carried away.
Tyson added: "The gaffer is making sure we are keeping our feet on the ground and we've got a lot of work to do."