Deane Smalley scored an extra-time penalty to defeat the non-league Tynesiders 1-0 in a first-round replay on Thursday night but it remains to be seen whether Wilder, who was given permission to speak to Portsmouth, will be in charge for Monday's second-round clash with Wrexham.
"The club have made a statement, and now it's between the manager and the chairman," said Lewis. "Football is football, we've got a lot of games coming up so we'll just worry about that.
"We're really proud of the boys, Gateshead are a good side - as good a football team as we'll see. We've had to sit off them a little bit, but we had a couple of chances as well. It's a really, really young side but the senior players saw them through well.
"We were hoping that we could nick a goal. They had more of the ball, but we were away from home with an inexperienced team."