Despite losing to Sheffield United in the play-off semi-final and missing out on a third consecutive promotion, Stevenage started the new campaign well and were among the top six as recently as December.
But a dismal run of results, in which Boro have taken 17 points from the last 69 available, has seen them tumble spectacularly down the table and closer to the relegation zone than the play-off places.
"After a very promising start with a new squad, we have slipped alarmingly and the board are concerned that the present management team may be unable to deliver the club's vision of increasing attendances and developing players in a winning environment," added Wallace.
"We have waited longer than most others in similar circumstances, but we cannot in all good conscience continue to watch this downward spiral and do nothing.
"It's time for a change and we'll see who applies for the position. Meanwhile, I'm indebted to skipper Mark Roberts who will, once again, step up and take charge whilst our search takes place."
Smith is the 33rd manager to be dismissed this season, a situation League Managers' Association chief executive Richard Bevan has
described as "embarrassing".
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