The rain and dark, overcast skies were an apt setting for President Reagan's long trip to appear at a rally and picnic here today on behalf of Sen. Orrin G. Hatch's (R-Utah) reelection campaign.

The president expressed disappointment that both the House and Senate had overridden his veto of a supplemental appropriations bill, but he vowed to "do a lot more vetoing" of "budget-busting bills."

Reagan's visit was a bit hollow for Hatch, who returned to Washington last night to cast what Reagan described as a "fruitless" vote to sustain the veto.

"I want to tell you something," Reagan told Utah GOP faithful at a rainy picnic and rally under the dark skies here. "They better practice at that overriding vetoes , because they're going to get a chance to do that every time they send an appropriation down that is over the budget."

Earlier, when reporters asked if the override indicated that he was losing his touch with Congress, Reagan responded, "No, I don't think so. I wasn't aiming for a scoreless game. I'll just be content to win . . . . Well, let's see the next time out."

A crowd of several thousand braved the rain to hear Reagan, who spoke from a platform positioned in front of bales of hay.

Reagan acknowledged to reporters that he was disappointed with the override and that he was hurt that Republicans had voted for it.

But at the picnic here he trained his fire on Democrats, continuing the theme that he and the GOP had taken strong actions since in office to set the nation on the right course. Current economic troubles, which he discussed only lightly here and yesterday in speeches in Kansas, are the legacy of generations of excessive taxing and spending, he said.

As much as Reagan attempted to direct attention at Democrats, reporters were unwilling to let him overlook the fact that Republicans in the Senate and House had made the difference in the override.

Asked if he harbored hard feelings against the Republicans who had voted against him, Reagan said, "No, I'm not angry. I'm just terribly hurt."

Later, when he was asked the question again, he said, "Oh, I wish they'd have behaved differently. But then everyone makes mistakes."

But if the events put a damper on Reagan's trip, they left Hatch absolutely crestfallen.

Last night Reagan, aware that he was losing in the Senate too, urged Hatch to return quickly to Washington to sustain the veto -- in effect to miss his own party.

The Utah senator had angled for months for the presidential visit to bolster his re-election campaign. Reagan's trip here had been scheduled, then postponed, three times. Yesterday, Hatch had tagged along with Reagan in Kansas, where Sens. Robert J. Dole and Nancy Landon Kassebaum had enjoyed the limelight. Today was to have been Hatch's turn.

"I have just really looked forward to this," Hatch told reporters before departing for Washington last night. "I am a little bit demoralized that I have to go."

Senior White House advisers had attempted to shrug off the defeat, saying that even the old Yankees sometimes lost a World Series. Because of the comparatively small number of dollars involved, the feat was more symbolic than real. The override opened another opportunity for Reagan to argue that, while he is trying to achieve fiscal austerity, Congress wants to keep on spending.

But White House aides said there were other issues involved. In the House, they said, the concern was over the appropriations for programs in the supplemental bill, especially for a senior citizen jobs program.

In the Senate, however, they said that senators felt it was their prerogative to determine how funds are allocated, so long as they stay within budget limits.