Despite Michy Batshuayi's early opener and Fikayo Tomori's second-half strike, the Blues had to endure a nervy end to the game after Kamil Grosicki pulled one back for the hosts with 12 minutes left.
Chelsea boss Lampard has expressed his frustration with his side's inability to put results beyond doubt as they look to keep their cup run going, stay in the Premier League's top four and compete in the Champions League.
And the former midfielder has urged the club to make the right moves in January to replace the quality they lost when Eden Hazard left to join Real Madrid last summer.
"There is no movement to speak of now," he told BT Sport. "We got a punishment in the summer and it is meant to hurt you.
"We lost certainly one of the biggest players in our history and one of the most effective and dominant players in terms of what he did. That is the situation.
"My job is to work every day on the training ground to make the players better and the other part for the club is how we move forward by bringing in players.
"We lost ground last summer, so we need to, for the short-term, push for this top four finish because I have a strong feeling where we can improve personnel-wise to take us forward. For me it's clear.
"The money of it is not my job but I have to be honest and truthful. Short term recruitment is something we have to get right."
Reflecting on his side's performance against their Championship opponents, Lampard said they should have had a bigger advantage at half-time and went on to make things difficult for themselves.
"I'm pleased. You can never take these games for granted," he told BBC Radio 5 Live. "There was a full house here. I know that is not always the norm so the atmosphere was bigger.
"In the first half Hull weren't great, and that's no disrespect because in the second half they were really good and put us under pressure.
"The first half was our time, when they were not quite at it, to finish the game. We had one-on-ones through the middle with their keeper. We got a little bit sloppy when we thought we were playing well and we didn't really capitalise on chances, which imparts a bit of pressure.
"The cup tie carried on into the 94th minute because of us and because Hull gave it everything to try and get back in the game.
"The game was in the balance [when we scored our second]. You could sense it. So yes, the second goal was big for us because it gave us a cushion."
Lampard added he feels "like a broken record" after seeing his side once again fail to kill off a game they were leading.