The game at the Coventry Building Society Arena looked set to finish goalless until Bobb produced a moment of individual quality in the 80th minute, cutting into the penalty area and curling his finish into the far corner.
Fulham had threatened earlier, with Josh King hitting the post, but clear opportunities were limited. The result moved Álvaro Arbeloa's side up to 12th in the Premier League, while Coventry remained 19th after eight matches.
Lampard felt his team had competed without doing enough to earn a victory, although he was disappointed that a tight contest ended without a point.
“Disappointed to lose. Can't stand here and say we should have won. A tight game without big chances for either team. We wanted to get a point out of the game we know all thee games are to9ugh. We weren't threatened too much. We didn't threaten them enough to give ourselves a chance of winning the game but then you just don't want to lose. Fair play it took a moment of quality from them to get the goal but disappointed to lose.”
The Coventry City manager acknowledged the quality of Bobb's decisive contribution.
“Good players when they stand you up in the box, he shifts it finds the small area that can give him a goal. Disappointed but also a moment of quality.”
Coventry also lost Bobby Thomas to injury during the first half, adding to the frustration of a difficult afternoon. Lampard said he did not yet know the extent of the problem and stressed that his squad would need resilience through a demanding campaign.
“We hope not too serious. I don't know the extent of the injury. We hope it's only a small injury.
“This season is going to be tough and we have to be robust and stay resilient in these moments. Tough week but we have to continue.”
For Arbeloa, the victory was further evidence that his players were learning to manage matches over the full 90 minutes. Fulham had suffered a late collapse against Ipswich earlier in October, but wins over Hull City and Coventry have offered a response.
“We are improving as a team,” Arbeloa said. “We are competing for 90 minutes.
“I told the players, it's not about if we play well 60 minutes or 30 minutes. We need to understand that you need to compete for 90 minutes, understand the game, understand what you have to do.”
Arbeloa acknowledged that Fulham had not created as many chances as in their previous match, but was pleased they remained patient until Bobb's opportunity arrived.
“Sometimes you win games because of the quality of your players,” he said. “I think it was a good game as a team but, at the end, the quality of Oscar in one moment decided the game.”
The late finish gave Fulham another three points and a second successive win, while Coventry were left to regroup after a contest Lampard believed his side had at least given themselves a chance to draw.