Transportation Secretary Neil Goldschmidt promised the Senate Banking Committee yesterday he will not use his office to "deprive people of funds or projects to which they are entitled," but said he still has a "personal problem" with Chicago Mayor Jane Byrne.

Goldschmidt appeared before the committee ostensibly to introduce President Carter's nominee for head of the Urban Mass Transportation Administraton, former Washington Metro General Manager Theodore C. Lutz.

But the real reason he was there was to counter criticism he has received since he declared Byrne untrustworthy Nov. 20 and said he would find other people in Chicago with whom to do business.

His remarks, made at a breakfast meeting with reporters, were widely interpreted to mean that people who do not support President Carter will find themselves on the short end when transit grants are passed out.

Goldschmidt declinded twice, under prodding from Committee Chairman Sen. William Proxmire (D-Wis.), to detail the root of his "personal problem" with Byrne, but said it predated her switch in allegiance from Carter to Sen. Edward M. Kennedy (D-Mass.).

"I intend to help Chicago without regard to my personal views about Bryne," Goldschmidt said.

One way he found recently to help Chicago was to hand out a $24.8 million highway grant in the office of Rep. Dan Rostenkowski (D-Ill.). Goldschmidt called Rostenkowski and asked if he could use his office to make the announcement.

Sen. Adlai E. Stevenson (D-Ill.) called that "unprecedented."

Goldschmidt replied, "I was not aware that what I learned was a regular practice in this government was a one-way street. I am often called by members of Congress to attend grant award ceremonies. I don't see that it's unprecedented at all."

"You aren't alone in having a personal problem with the mayor of Chicago," Stevenson said.

Everybody agreed that Lutz was eminently qualified to be UMTA administrator, and Sen. Harrison Williams (D-N.J.) predicted after the hearing that the Goldschmidt-Byrne flap would not "spill over" onto Lutz's nomination chances. He predicted the Senate would confirm Lutz's nomination by the end of next week. CAPTION: Picture, NEIL GOLDSCHMIDT . . . problem with Byrne is "personal"