The Eagles became the first team to get the better of Leverkusen in their own back yard this season in the Bundesliga, moving three points away from the relegation zone as a result.
However, Veh knows there is still a lot of work to be done if they are to avoid relegation this season.
"Absolutely. We're totally happy that we've gone through (to the last 32) in the Europa League, and that we're through (to the quarter-finals) in the DFB-Pokal, but things aren't going to get any easier," he said.
"If we manage to keep three teams behind us, then we will have learnt something from this season."
Their struggles were predictable, according to Veh, who expects them to endure in 2014 as they continue to seek the fine balance between all three competitions they are playing in.
"It's the down side to a good deed," he told Sky television. "A team is promoted, they qualify for Europe and then you get problems, but I knew this.
"We can no longer play the kind of football we could play when we only had the Bundesliga to prepare for each week, which is why it is going to be a difficult Bundesliga season for us."