Veh on Monday confirmed that he will not be extending his contract with the Eagles, which expires in June.
He will be leaving the club in the summer - three years after taking charge, having guided them into the Bundesliga and straight into the Europa League - optimistic he will be leaving behind a side still in the top flight of German football.
"It's important to me that we reach our goal for the season, which is survival, in spite of all the burdens and problems," Veh said at a press conference in Frankfurt.
"I cannot imagine my departure having a negative impact on the team. Jupp Heynckes went on to win everything after announcing he was leaving Bayern (last year)."
Veh revealed how he had made his decision during the winter training camp in Abu Dhabi, but had agreed with the club not to make any announcement before the news was leaked over the weekend.
"I only informed the team that I'm leaving (on Monday)," Veh said. "I wanted to announce it in the winter, but I agreed to the club's wish to do so later.
"It's not true that I told the players before Sunday's game."
Before he does leave, Veh's job is to ensure the club do not go down. Sunday's win gave them a six-point cushion over the relegation zone with 11 games of the season remaining.
"We all have the desire to work together successfully right up until June 30," club president Heribert Bruchhagen said.
"We always wanted to extend his contract, but he told us in Abu Dhabi that he would not be doing so.
"Given the sporting situation, we decided to put back any announcement."
Veh has already been linked with a move to Bundesliga rivals Schalke, whose coach Jens Keller is under pressure following two heavy defeats last week.
Frankfurt have yet to identify a replacement, although it is one of their priorities to do so.
"We haven't spoken to anybody yet, but the position of head coach is a very important one - especially in terms of players' contracts and new signings," said the club's general manager Bruno Hubner, who is not aware of any of Veh's assistants also wanting to leave.
"We can only speculate about the current coaching staff. It will all depend on who takes over as head coach."