Posh, who currently sit fourth in the third tier, face Charlton at home on Saturday before travelling to Southampton for their next league game the following weekend.
Johnson says his team must play their own game if they are going to gain positive results against the in-form duo.
He told the Peterborough Evening Telegraph: "Charlton and Southampton would certainly be classed as two of the biggest clubs at League One level and are undoubtedly two of the best-supported.
"Charlton have had a good little run of late and Southampton have hit a bit of form, so it has worked out that we are catching these two teams at a time when they've been picking up a few results. We haven't had a consistent run of form as yet ourselves, but hopefully that will happen soon.
"If we can come through the next two league games unscathed, we could find ourselves in a very good position. It is definitely something we are capable of doing. They are both the type of matches which we need to look forward to and not fear. It is up to us to play our game and see how the other teams handle it."
Source: PA
Source: PA